Twitch is probably in my top 3 of all time favorite characters. Why? Becuase he is just cheap enough to work! His stealth ability (His 'Q') is probably the most overpowered ability ever (Maybe besider Tryndamere's Ultimate). He can straight up appear out of now where behind you, count to three and you'll be dead. Probably the most irritating thing in the world! But if you master him, you'll drop pentakills like it's your friggin' job.

I usually start with Doran's Blade because Twitch isn't the most damage friendly champion, you have to kind of give him that little boost. Because of this, I usually have 3-5 kills by the ten minutes mark.
Secondly I like to go for the Boots of Mobility. Why? Because if you get ganked at all, you can switch on your Q, hope they don't hit you and keep you out of stealth, and if so, it's a clean get-a-way,. I love these boots because you can move at almost 500 movement speed when stealthed, which makes it perfect if you need to get somewhere to gank or what need-be. Not to mention they help you position yourself softly behind the enemy champion, until you start unloading on them without warning!
Next, I like to build to the Phantom Dancer. For any DPS character, this is almost mandatory, with few exceptions. Twitch needs this to become faster for the kills. I also build this first before any major damage boosting items because his Q gives him even more attack speed along with his E, which is a nice finishing blow move, so attack damage isn't a necessity yet.
After that, I like to then start building for a montage of B.F. Sword builds. I get the Infinity edge for the massive attack damage increase along with the amazing 250% crit bonus, which goes hand-in-hand with the Phantom Dancers, then I go for the Black Cleaver for, obviously, more attack damage and then a little more attack speed, then I finalize the B.F. Sword collection with The Bloodthirster for that nice bit of life steal.
Ok, so if you've gotten this far, you're doing well and you're also probably twenty-some odd kills positive. At this point I sell my Doran's Blade and buy some Warmog's!

Your 'Q' will make your game. The reason I max it first is because that's the longer you can stay stealthed and the longer you have to scout out possibly hidden enemies, not to mention it really saves mana. Secondly I max the 'E'. This spell is awesome. This is the spell you want to finish your targets with. If you get them remotely low health (which is what you want to do before using your 'E') then you want to slam that 'E' button real hard. This spell has such a massive Area of Effect (or AoE), it's nearly impossible for anyone to run away from you if you instigated a fight.
Next, of course, it will be your ultimate that will be maxed. This ultimate reminds me of Kog'Maw's 'W' ability. Basically giving you super range, again making it almost impossible for the enemy to run form you!
Lastly, (but not leastly!...wait...) you want to finalize with your 'W'. Many may disagree with this and at least give it one point early game for the slow, but honestly, with this overall build, you won't have to worry about slowing someone, you'll kill em' too fast! Even towards end-game when I'm level 18 and even fed, I rarely find myself using this spell.

I use Flash for the quick get-a-ways in case you get ganked. It comes in handy if you get chased by a bunch of enemies. Your Q only activates if you aren't being hit by something for a second or two, so this Spell makes it perfect for an attempted get-a-way with a 'Q' to makes sure you stay alive!
I use heal because Twitch is kind of squishy, not to mention, who doesn't like a little survivability!?

Pros:
Super fun to play with! :D
Can go stealth mode for 10/20/30/40/50 seconds at a time, pending on level, making him very hard to find, and even initiate on.
Has very large range AoE's that make him great for chasing and finishing off potential kills.
His 'Q' gives him a very high rate of fire, mixed with Phantom Dancers, it makes him hit super fast.
If given a nice amount of attack damage, he will most likely 4-6 hit every champion in the game as long as they aren't stacking armor or health, and yes, even tanks.
He is super easy to get fed with. The best part, is you feed off of champion kills! Not minions!

Cons:
He is very squishy. (Not much armor, usually an easy kill).
He doesn't have a lot of health.
His stealth can only be activated when not under attack.

With this build, it is super easy to use your 'Q' and go stealth mode, walk up behind an enemy champion to try to cut them off when they try to run to their tower, and just unload on them with your massive attack damage and speed. Not to mention, who cares if they get past their tower into what they consider a "Safe Zone," just use your E!