As of today, 2/15/2012...I've improved the item build, given additional details and more guidance. I hope you like the changes! Please comment when you get the chance and remember, do not vote until you try it out a number of times :)

I can't stress this enough, the Greater Quintessences of Vampirism are essential for a jungling Twitch. DON'T BOTHER JUNGLING TWITCH WITHOUT THEM! I suppose you could try armor Quints but Vampirism definitely outperforms them all game long. With 3 Quints, your life stealing mastery, and a Vampiric Scepter you've got 21% life steal at level 1. You can easily gank several times between levels 1-6. I highly recommend that experienced players follow the item build I've laid out, get a leash at red, and then gank bot or mid at level 2. Unless...you want to sit invisible in the bot brush your two team mates for first blood and a possible double kill at level 1 ;). Continue ganking a LOT...you should not wait until level 6 to gank if you follow the item build I've laid out. Just make sure you don't tower dive. If your teammates are overextending...make them get wards or back off with last hits so you can gank.

If your just learning how to jungle with Twitch then I suggest starting with Cloth Armor and 3-5 health pots. I'd still recommend starting at red with a leash. If you choose not to gank, then go for the wraiths, wolves and then blue. After that, feel free to roam back to wraiths, gank or heal up. If you go the cloth armor route...I suggest jungling until you have 685 gold. Then, recall and buy Madred's Razors. After that, follow the item build I've laid out. Upgrade that Madred's Razor to Wriggle's Lantern or if you started with a Vampiric Scepter I'd suggest picking up Executioner's Calling.

One last note. Once you become even more experienced and really want to mess up the other team's jungler...start at THEIR red. How do you do that? Well, pickup the Vampiric Scepter and quickly rush to their red. For videos about how to do this...check out this very popular Jungle Twitch video: http://www.youtube.com/watch?feature=player_embedded&v=sYIsy7s3p9E
If you want to skip to the part about taking their red...start watching from 2:20. Also note, this video comes from the very well known jungling guide: http://www.mobafire.com/league-of-legends/build/a-jungle-twitch-is-a-happy-twitch-137451
I disagree with his item build but he does have a lot of good tips about jungling with Twitch.

Essentially, you don't sit in the bush directly above their red. Instead, you hide in the brush just above it and to the right. After you steal their red you should proceed directly to top for a gank. If you don't get the kill...you should harass top hard enough to force them to burn their flash. Then, you should go for your own blue and roam back to top to finish them off. Why does this work? Most players are dumb enough to think you left. Since they didn't go back to base, they don't have a any regular or vision wards either. Can we say...FIRST BLOOD?!? ;)

Although I haven't added them in at any specific point, do not forget to buy wards. Be sure to place them at their buffs if they have a jungler so you can gank them as much as possible in their own jungle. NEVER UNDERESTIMATE THE POWER A 75 GOLD WARD CAN GIVE YOU! I tend to buy them all game long. What I'll do every time I go back to base is buy an item or the items I need and then use the leftover gold to pickup a few wards. Learning how to manage wards simply takes time and practice and there are plenty of guides on how to place them :)

I'm sure you have questions about why I chose the items that I chose and why are they in the order that I listed them in. So...let's go through it! We start with a Vampiric Scepter...this allows you to jungle with ease and survive the ganks you want to do. Depending on the option for ganks I may not go back to base for quite a while...in which case I'd just save up for the most expensive damage item I can buy when I do go back such as a pickaxe or bf sword. Otherwise...I'll probably do a gank, head back to base and buy the next item in the build order. KEEP THIS IN MIND...IF YOU GANK A LOT YOU SHOULD GET A DORAN'S BLADE TO START. I frequently start with a Doran's blade and start saving up for a pickaxe. I change gears if my team fails hard or I'm failing hard and get the items that let you farm up as listed in the item build order.

I buy Executioner's Calling because it improves your jungling ability, gives you impressive crit early game and allows you to Grievous Wound your gank target every time you gank. Everything it offers for the low price of 1350 is a BARGAIN! I'd say it's the most overlooked item in the game and easily one of the most powerful to use all game long because of Grievous Wound's scaling against life steal, hp regen and spell vamp. Almost every champ has some form of regen, spell vamp or life steal and this item reduces it by 50%! Honestly, I think this item is way too overpowered and way too cheap...hopefully it doesn't get nerfed ;)

After Executioner's Calling we upgrade our boots right? I used to pickup boots of mobility and they really are a good choice. I recently switched to the Berserker's Boots because the extra attack speed, mixed with Phantom Dancer, allows me to hit about 2.3 AS when I come out of invis instead of 2.1. One thing to note though...I rarely upgrade my boots before I get the Infinity Edge. Why? I gank a lot and stay out long enough to buy damage based items that will improve my ability to gank. Damage and crit will do a LOT more for you than the attack speed from the boots. However...if you fail to gank, the ganks fail or your teammates are feeding the other jungler kills because they refuse to stop over-extending...then you'll want to upgrade your boots because you need speed to move from one jungling camp to the next as quickly as possible.

We've come to the Infinity Edge...your first expensive item! Once you get this item...you should be a HUGE threat in the other team's view. You do massive damage with it and combined with the attack speed of ambush you should be able to take out anyone but the tank on the opposing team. If you ganked well up to this point...you could probably even take out their tank too ;)

Then we proceed to work towards our 2nd Infinity Edge while weaving in the precursor Zeal to the upgrade of Phantom Dancer. But the real question is...why are we buying a 2nd Infinity Edge? Simple it gives you 80 dmg and 25% crit...with two Infinity Edges you have ALL THE DAMAGE YOU'LL EVER NEED. Combined with Phantom Dancer and Executioner's Calling your crit will be at 95% your base damage at about 287 and your life steal at 27%. This is all BEFORE YOU GET YOUR LAST ITEM...that means you dish out insane damage and you do it well before a full build! This gives you a huge advantage over the opposing team and allows you to carry hard, in addition to all the roles you take on as a jungler :). Each shot you fire will be a crit and will do 746dmg without any buffs. If you get the red or baron buff...you can expect that to come close to the 1k mark. So, back to the question...why do we get 2 infinity edge's? Simple, we want max damage via having MAX CRIT! Who cares if you can get a higher base damage if you don't crit on every shot? Constant crits will always out damage any other option in my humble opinion. The only thing that somewhat affects your damage is armor. But honestly, armor doesn't matter simply because the tank and possibly the bruiser are the only ones that get it and you should NEVER FOCUS THE TANK anyway. Simply come out of your invis, pop your ult and fire 2 well placed shots on the carries and support and they will die. At that point your whole team focuses on the tank and bruiser and as you will observe...armor won't matter at that point ;)

This leaves us with the all important question, what's the last item I should get...IF YOU GET THAT FAR IN YOUR GAME!

Ah yes, how do we decide which item will be our last....

First of all, if you're playing jungle Twitch right then your games are ending well before you can buy your last item. If you have to buy your last item then one of two things is most likely true:
a) Your team had a very rough game. You had a feeder, your team mates constantly over-extend and failed to ward their lane while doing it or both.
b) You somehow didn't get fed because you failed your ganks, you failed to gank enough, or your team couldn't coordinate ganks well with you.

Either way, you're in the position of buying your last item. Observe the opposing team's items carefully and choose wisely. Picking up another offensive item is overkill. In addition, defensive items are fairly useless on Twitch. So what do you do!?! Well there is one HUGE EXCEPTION...ZHONYA'S HOURGLASS! Take this item to any team fight and here's what you will do:
1) Go invis
2) Pop your ult (This takes you out of invis)
3) Fire at the carries/support with one shot at the rest of the team
4) Flash backwards the moment you are focused and activate ZHONYA'S HOURGLASS
5) Pop Expunge when the Hourglass active runs out and PENTAKILL WOHOO!
If you have Kayle on your team, and he's smart enough to immune you with his ult, then you won't need this item. Otherwise...get it and enjoy the show!

There is one other defensive item you could consider and that's Warmog's Armor. With this item you have to farm up some minion kills as fast as you can and then join the team fights. The advantage to this item vs BloodThirster...is you NEVER LOOSE YOUR STACKS. That's great for squishies who tend to frequently die. Also, this item is a perfect choice if you will be split pushing or back dooring. With it, you may or may not be able to survive a team fight, it depends on how well you position yourself and how capable your support/tank are. Just remember, your goal in a team fight should be to stack poison as fast as you can. Then, pop expunge at just the right time to get that pentakill. Of course...you don't have to be the one to get all or any of the kills...you could pop expunge early so that your team mates enjoy the feeding too :)

Your other item choices are offensive. If you really need to tear a tank down fast, even though you should never focus the tank in a team fight anyway, you could pickup Last Whisper, the Black Cleaver or Madreds. It is possible they could be a troll team of all tanks or they have a lot of beefy bruisers. Both cases could call for the items. If it were me, I'd pickup Last Whisper and upgrade to Madreds if they have high HP and the game drags out. It's cheap...which allows you to take advantage of its benefits significantly sooner than the other two items. It gives you the largest armor reduction but doesn't give you attack speed. To restate facts...you'll be sitting at 2.3 AS by the time you pickup your 5th item when you come out of invis. More attack speed is just overkill at this point. But having a huge armor reduction would allow you to 2-4shot the freakin tanks LOL! Remember, each of your shots will be a crit and with the extra base damage they will be up around 850+ unbuffed. Couple that with the armor reduction and BAM tanks will die lol. Like I suggested earlier though...picking any offensive item at this point is overkill. Recall your goal for team fights is to stack poison as fast as you can and deal out all your damage before you DIE. Funny thing is, Twitch is EXTREMELY SQUISHY. Who cares if you have all the damage in the world when you can't deal it out because you are DEAD. This is why the BloodThirster is useless since you have to farm up the stacks and then loose them every time you die. Hence, I recommend picking up a defensive item or...as I explain next a CC item.

CC? What the **** is that? Crowd control. It's those annoying abilitys that disable you or prevent you from doing what you need to do in a fight. To prevent these effects you could get the Banshee Veil or Quicksilver Sash. There are cases where these will help you win a team fight. In most cases, by the time you cleanse yourself with a Quicksilver Sash or block a worthless ability with Banshee Veil you'll be dead. A poor...dead....squishy.

Honestly, the last item that I tend to pick the most now is ZHONYA'S HOURGLASS. The 100 ability power does make that expunge hit harder and it's hillarious to watch the other team focus you until you pop the active and then laugh because they have no clue what to do while your teammates destroy them. You've become the UNKILLABLE SQUISHY! Your only concern is heavy cc which is why you NEVER initiate and ALWAYS STAY BEHIND YOUR TEAM FOR TEAM FIGHTS. Let the other team cc the **** out of your tank when he and your bruisers initiate, then proceed to join the team fight. If you pickup Warmog's Armor...you're just as unstoppable since each shot you fire does 800+ dmg and gives you 216 health per shot. At max stacks with Warmog's you'll have 3010 life...couple that with your damage, life steal, poison, expunge and GRIEVOUS WOUND...you're pretty much UNKILLABLE!

I follow the sequence I've laid out because it maximizes the lvl 1-6 ganks. Attack speed and slow are significantly more important than a highly leveled expunge for early to mid game. Why? You'll land your poison stacks much faster and will be able to expunge at the full 6 stacks on two enemies dealing more over all damage anyway. Secondly, I've found the attack speed is of a greater benefit to killing the jungle mobs than expunge is.

Your ideal gank sequence at level 2 would be invis...and then pop out of invis by attacking your target at the same time or slightly before your team mates. If your team mates have cc let them use it. The moment it runs out, pop your slow and fire until your poison will finish off your target before you turn to the next target.

Your involvement with Team Fights is important to manage. Sometimes you're present, other times you let your 4 team mates push a lane. Meanwhile, you draw the opposing team to the lane you're back dooring because the other team hates you so much. Split pushing and back dooring as I've described are important to weave in to a game. However, be very careful about doing it if:
a) Your team had a very rough game. You had a feeder, there's a lack of coordination, or both.
b) You somehow didn't get fed because you failed your ganks, you failed to gank enough, or your team couldn't coordinate ganks well with you.

When you find yourself joining team fights you must not forget two things: Your objective and your squishiness. You are EXTREMELY SQUISHY and your goal in a team fight is to survive long enough to land your all important combo. To do this, you MUST ALLOW YOUR TANK/BRUISERS to initiate. NEVER initiate. If you initiate, you'll most likely cost your team the fight. Let the other team cc the **** out of your tank when he and your bruisers initiate, then proceed to join the team fight. Before you join the fight, you should already be roaming around the area while invis. You'll then activate your ult (bringing you out of invis and activating your attack speed), then slow and follow up with expunge after your ult shots run out. If you were smart, and stayed well enough behind your tank, you will not die.

This should be common knowledge but in case it isn't...DO NOT FOCUS THEIR TANK. Fire at the carries and/or support.

One last thought for this section. On rare occasions where you are extremely fed and/or the other team is coordinating poorly, you could position yourself behind their team in order to 2-3 shot their squishies. Keep in mind that this positioning should be extremely rare and you'll most likely cost your team the fight if you try it. If you attempt this position you still cannot initiate unless you really want to feed the opposing team.

This guide isn't completely exhaustive but is meant to give you a good idea on how to jungle with Twitch. If you're looking for a fully comprehensive guide I'd suggest checking this one out: http://www.mobafire.com/league-of-legends/build/a-jungle-twitch-is-a-happy-twitch-137451

Although I disagree entirely with his main item build, he has a good point of view to consider on how to jungle with Twitch. He also includes some videos :D