The game has started

Regardless of whether you started the game on the red or blue side, it is always worth starting with the red (especially when playing on the bottom side, because it will give you a chance to top ganks, which on level 3 is the easiest lane to assist. Moreover, on lower elo - let's say somewhere to low platinum - you will have a huge chance for stealing enemy red buff. To do so, after your red, go straight down for enemy red, use Q on it, kill it and go back to your jungle. It will give you a small advantage. If it's not warded, you will most likely success, because nowadays many junglers goes for full clear.
You reached level 3 - now it's your job to kill scuttle crab and do gank on lane (as I said earlier, best option will be top lane). If it's possible, kill both scuttle crabs - you will have sligltly more gold and undoubtly higher level, which can win early stage of the game.
Now it's time for reset - if You killed someone, it's most likely you can rush Warhammer and 1 / 2 control wards. At this time you have level 4 or 5,
I always try to do sneaky drake, no matter which side I am. Place a control ward in pit, make sure your allies make pressure on lanes and try to kill it. With your kit you can easily lifesteal incoming damage (especially when you fight Infernal and Mountain drake, because their attack speed is low enough to always prepare your shield). Keep in mind, that as a Lee Sin you are always quite safe, even if enemies will come. Use trinket + W to run away when you will be in trouble. If you were unlucky and your enemy started doing drake, try to steal it - especially when you are on red side. In the early stages I always recommend throwing your Q when drake is at about 700-900 health.
Scuttles done, drake done, first gank done. Now you have to farm your way to level 6 and process more ganks. From this point I suggest visiting bot lane, because your current kit allows you to do a good gank and make successful 3v2 or 3v3 (if enemy jungler come) gank.

A risk I shall take

From this point, try to fight as much as you can, and when you will have a break, do some camps to stay up with your level. In fact, if you were ahead in early game (or at least even), from level 8 You can basically stay in your jungle with full hp bar, thanks to level 2 max W (it gives you decent shield and good lifesteal).
Force Rift herald, in most cases use it as fast as you can on pushing lane (well, you need your trinkets). Secure all drakes, give your third blue to your mid laner. If you aren't skilled enough, don't force unnecessary plays. I had this problem as well - back in the time I thought I am enough good to pull out some fancy insecs and generally flashy plays for style points. Yes, if you have good muscle memory after hundreds of matches, you can go for it. But use your kit wisely - one bad decision and you will be probably punished hard for that (especially in current meta, when you can get CC chained). You can always peel for your team and kick away enemy assasin from your ADC. Remember - focus on objectives and map control. Always buy at least 1 control ward on your back - 75g is worth map control, but also giving you an opportunity for ganking or escaping.

Worry not

Nightmare of every Lee Sin casual. From this point you will lack damage in close fights against most bruisers. However, if you reached higher level, You can fight most of the fighters. Avoid duels with assasins like Kha'zix or Rengar, at this stage they can one shot you. However you can try to kill vulnerable mages with no dashes, same goes for adcs and top laners. Safety way will be ward jump --> land Q --> press R --> press q once again
Try to get one inhibitor, best option will be forcing either bot or top inhib, because it will give you opportunity to do safety drakes / baron

Fear clouds your mind

Tips for begginers:

1. Always try to start your gank with trinket + W close to your enemy. Hold Your Q, because enemy will most probably flash. Moreover, enemies quite often tries to "overdodge" your Q. What does it mean? They will try to sidestep and dodge your Q, but at the same time, you can just auto them to death
2. Do flash kick, instead of kick flash. I know all of you want to style on enemies, but that's not the point. You will end up probably missclicking your combo, and in fact wasting your flash. Do flash kick - it's still fast and in 90% cases your opponent won't use his flash or dash fast enough.
3. Go for plays in minion waves. Sounds stupidly easy, but I saw many Lee Sins going for insecs completely mindlessly (no minion wave, no teammates nearby, etc). Calm down and pull out your plays only, when you are assisted by your teammates
4. Predict. If you see for example LeBlanc using W, throw your Q in the place, where she was at the beginning. If you see Ezreal running from you, throw your Q ahead. By the time you will know most champions typical movement. Practise it on classic game mode.

Tips for players with experience

1. If you are going for insec, hit your Q in a person other than the one you want to kick. On higher elo, enemy mages and ADC will be prepared for your actions. Hit Q on a support or tank, you will make enemy carry feel safe. Then go for a fast combo
2. If you land Q on something and you will be ready for go in, take a few steps back. Again, you will make your opponents feel safety and comfortable, then go in.
3. Change the trajectory of your 'flight'. What does it mean? Enemies will most probably prepare their CC, when you will go straight on someone. Use your trinket + W to change your current location and force your enemies to miss, then use Q.

Pros:
- high mobility
- decent early and strong mid game
- sustain and ability to stay in jungle for long
- countless combos
- versatile hero, you can build lot's of situational items
- ability to steal objectives and push towers with your passive

Cons:
- vulnerable to any kind of hard CC
- if you missclick, you end up dying
- you have to be decent Lee Sin player in general to be useful in late game
- easy to play, hard to master

Master yourself, master the enemy

So, why would you even listen to me? I can't answer this question, because I am not a Gripex, Heizman, Insec and one of many other great Lee Sin mains. However I reached Diamond - it's not particularly high elo, but it's high enough I gained some experience, which I wanted to share with you. Playing League, and especially Lee Sin, is my passion. You can look up to my statistics - when I'm writing this guide, I have 61% wr in over 160 games as a Lee Sin. Link to statistics:
LeagueOfGraphs

I also did my first montage video on Lee Sin and in the nearest future I want to expand my content. Video down below Play Video
And remember - you don't have to proof anything. You don't have to pull out spectacular plays. Do your job, improve, watch your replays, correct mistakes and learn more and more combos
I think it's all I wanted to share with You. I hope you enjoyed this guide and you will find it usefull. If you have any questions, you can start a discussion here, or add me in game. Nickname - D3str0 on Eune server.