A few things to take note of when playing Lee Sin as a jungler:
1.) Lee Sin is OP -- accept and abuse this fact
This is all you need to know when playing Lee Sin as a jungler...
Very few junglers are able to go toe to toe with Lee Sin when played well, such as:
-Udyr
-Trundle
-Skarner
-Olaf (rarely done anymore, but still a threat in 1v1 situations)
-Lee Sin (if you're not in Ranked)
Not to say you Cant fight these junglers 1v1 -- especially early game. These are merely the champions to be careful with should you choose to counter jungle early (like I tend to do).

I choose to go 21/9/0 mostly because of my tendency to counter-jungle at level 2, but if I know who the enemy jungler is, I'll either stick with these masteries and attempt the level 2 invasion/gank for first blood (and start to snowball), or 9/21/0 if I think I'll have a harder time keeping up with my opponent for counter-ganking, or if our team simply needs a slightly more sustainable partner in ganks and/or team fights.

Ok, here's where your early game is determined. If you KNOW your team mates are somewhat competent in their ability to help you with your jungle, start Boots and 3 pots for speed and ganking potential -- as your health wont get too low. Additionally, your ability to counter-jungle early on is a lot stronger.
Otherwise, taking Cloth armor and 5 health pots is pretty standard on anyone -- especially if you're new to jungling.
If you're able to get first blood or any kind of kill before your first trip back, you should have no problem picking up 2 Dorans blades (but I'll always take at Least 1 before moving onto my next item). Dorans gives you sustainability, damage, and the lifesteal stacks decently with your W. I dont suggest getting a 3rd Dorans Blade unless you're really hurting in farm and really need the extra health, damage, and lifesteal.
First real item after your Dorans Blade(s) will almost always be Phage. Yes, your E and Red Buff helps you stick to your enemies easily when ganking, but the additional procs help that much more -- and you're mostly getting it for the bonus health and damage.
Now you're gonna finish those boots of yours. If your enemy team is more AP or CC based, get your Mercs, and if they're more AD based, pick up your Tabi.
NOW -- This is a critical point for you. If you're starting to dominate the game (which you should be, you're Lee Sin!) I tend to rush a Last Whisper to keep up my damage output before people are able to build up armor and start to counter you. Otherwise, I'll either pick up Giants Belt and Then Last Whisper, or finish off Frozen Mallet before Last Whisper if we're having more trouble sticking to people in team fights.
At this point, your damage output is pretty significant, especially if your team has been able to snowball with you off of your ganks and teamwork. Should the game continue any longer, its time to trade in those Dorans Blades for either a Bloodthirster or Warmogs (again, if you're dominating the game, keep up with the damage output, otherwise, build Warmogs and focus better in team fights, and of course follow it up with the other item (if you get BT first, get Warmogs next, and vice versa).
The last item is situational, as you can tell by there being only 5 completed items in the build above. Most likely these items can typically be one of either Amtas Impaler, Randuins Omen, Maw of Malmortius, or Trinity Force. But its completely up to you, these are just the items I tend to build as a final item on Lee Sin.

WHY NO WRIGGLES?!
I've just never needed it with Lee Sin. It helps with early Dragon control and it gives me a free ward to jump to, but once you get your positioning down you dont need the ward for emergencies, and you'll be putting out plenty of wards already. Also, your damage output on Lee Sin is high enough to send bot lane back (if not Kill them) in a gank, and then you'll be able to take Dragon a lot easier.
Its your call of course to build Wriggles, but you'll always trade it in later for a bigger item. This is just My opinion on Wriggles..

I'll almost Always start E on Lee Sin when jungling and start Wraiths (as does 99.99% of all other jungle Lee's), unless we're invading, in which case I may take Q.
And if you start E, then at level 2 you can choose to either get Q and go for a gank/counter-jungle (best if you have boots) or W to stay in the jungle a bit longer. I personally prefer getting W at level 2 if the enemy jungler is someone with a lot of invading potential like Udyr or Trundle, but otherwise it's better to get Q at level 2 (again, just a personal preference in play style).
Then I'll typically max Q then E before W (picking up R whenever possible of course). However, I've recently been testing out maxing E first before Q, as it typically makes your damage output more reliable (if you miss your Q, the majority of your damage still comes from an AoE ability, and makes you stick to your opponent better than maxing Q, at the cost of losing some damage if you Are able to land your Q)

I prefer to take Exhaust over Flash for a few reasons.
1: Exhaust has a lower cooldown than Flash, meaning if you trade your Exhaust for the opponent's Flash in a gank, you'll be able to gank again With Exhaust before their Flash is back up.
2: While Flash is really useful for getting out of dangerous situations, or quickly jumping over an enemy to kick them back into your team, etc, I find Exhaust much more useful during the early game when Lee Sin shines the most, and using Exhaust makes it much easier to snowball into the late game much faster than with Flash.

Other viable spells to use while jungling include Teleport, or even Heal

Alright, There's a few different ways to jungle with Lee Sin.

1: Wraiths - Red - Golems - Wraiths - Wolves - Blue etc, taking any opportunities to gank. A pretty standard circuit for non-mana users in the jungle

2: Wraiths - Red - Wolves - counter-jungle. This is the route I typically take when the enemy jungler starts at Blue and gets low enough to kill easily at their Red (Alistar, Fiddlesticks, Gangplank, Hecarim, Maokai, etc). Depending on the speed of the jungler, you may have to skip Wolves and just head straight to the enemy Red buff with E and Q.
NOTE: If your team gives you a strong enough leash on Your Red, and you're able to save Smite, and you have enough time to do Wolves and catch the enemy at their Red, it's relatively easy to smite steal the enemy red and get level 3, making the kill even easier.

3: Wolves - Blue - Enemy Golems - gank the enemy jungler With Your Mid and/or Top. Another really easy way to get first blood and set the enemy jungler way behind. The problem with this tactic is you typically dont have red buff (unless the enemy jungler is extremely slow and you're able to take it before they get to it. But also, this requires your mid and/or top to push hard and disappear for a bit, which makes it really obvious and Should alert the enemy team, but still very effective.

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MY NEW ROUTE!!
4: Golems - Red - Wraiths - Wolves - Invade
For this route you need Boots + 3 Pots, and be jungling against someone that you can take in 1v1 combat that starts at Blue buff.
Start E, then W (to keep your health up) then Q at Wolves, then instantly invade the enemy jungle at their Red. 99% of the time they'll be finishing their red buff just as you arrive. (when jungling against someone Faster, get more damage on your Golems and Red buff) to clear your route in time to catch the enemy before the go back)

A few basic notes for newer junglers:
1: FARMING IS YOUR FIRST PRIORITY -- NOT GANKING!!
The point of having a Jungler is to have 2 solo lanes (Top and Mid), NOT to have someone that can gank whenever they want. If you fall behind in levels, you might as well have had no jungler at all...
2: IF YOU'RE GOING TO GANK, GANK ASAP, DONT STAND AROUND WASTING TIME!!
Wasting time standing in a bush waiting for a chance to gank is time that you're not farming and getting Gold and Exp. Its a lot easier to fall behind the enemy than it is to snowball and carry. If you're not used to jungling, you might as well farm until someone flat out Asks for a gank.
3: KNOW YOUR ENEMY -- WATCH THE LANES!!
Knowing the typical routes each jungler takes and when and where they'll show up for a gank is crucial! Be prepared to counter-gank, and position yourself accordingly. Lee Sin is one of the strongest champions to counter-gank with, and can easily turn the tides of a 2v2 or 3v3 situation.
4: PRACTICE!!
Playing a specific champion in the jungle can be very frustrating. For me, Nocturne was a nightmare to play with, between using his Ultimate and baiting spells out for his Spell Shield, etc, I was playing like a total newb for my first 10 games or so. Now hes one of my main champions in the jungle, and easiest to get first blood with.
Dont get discouraged, keep up the hard work, and you'll get the hang of it.