I hit Gold in Preseason 10 using Yi and Jax almost exclusively to climb. Here's how youc an do the same!

You want Red Bloodrazor and Rageblade right now because the passive on Rageblade is too strong compared to other options. (Standard Build). If you want to build crit instead then a Warrior plus your standard IE + Statik will help you do damage.

In teamfights Yi will struggle with CC so make sure you have some defensive items.
Stopwatch can be really good on Yi if you are using your Highlander(R) to engage and soak up damage and then heal using Meditate(W) once your team follows up.

Although Yi is an assassin-carry, carries still need to stay alive to deal damage; and since Yi lacks escape like Talon or Ekko, you might want to build some pure defensive items if you need to carry 1v9.

Bloodrazor:
Always take bloodrazor on your standard build. Take blue if you think you will have trouble engaging/ deal dps. Otherwise take red because the damage is better.

Rageblade:
A core item on Yi. Rageblade passive resets Q, and synergizes with Double Strike passive.

Merc Treads/ Tabis:
Provide Yi with cheap defense. Better than Beserker's imo.

Death's dance:
helps Yi soak up damage in a teamfight and you can reduce the bleed with meditate. Also provides lifesteal.

BORK:
death's dance is better unless they are all very tanky.

Wit's End:
Great on Yi. Will help him survive in clutch teamfights.

Guardian Angel:
Great item.

Zhonya's:
Also great item if you need stopwatch passive more than GA. Synergizes with Death's Dance.

Stopwatch:
Broken generally.

Maw/Sterak's:
Can be helpful if enemy has burst. Stopwatch is better but if you need the shield a lot consider Maw or Sterak's.

QSS:
Great item if enemy has lots of CC. If you build Scimitar, don't build Death's Dance.

Randuin's:
Useful if enemy has a Vayne or fed Cait. Also useful for the slow.

Spirit Visage:
Wit's End is better unless you really need the HP.

Runes:
Precision

Conqueror:
Too broken to consider other runes. Of course, if building crit, hail of blade is better.

Triumph:
For those clutch towerdives/teamfights.

Alacrity vs Tenacity:
Alacrity is better generally, but tenacity is useful against a heacy cc comp.

Last stand: better than coup de grace atm

Domination

Taste of Blood: heals you when you do damage (including on-hit damage)

Eyeball collection vs zombie ward: take eyeball unless you really like the team aspect of league of legends soloq.

You want to full clear your jungle pre level 6 and if you know you can cheese gank/invade then an early game kill can really help Yi snowball.

Champions you want to avoid dueling early:
- Udyr
- Xin Zhao
- Lee Sin
- Jax (with Counter Strike)
- Nocturne (when he's almost 6)
- Rammus

Yi also clears objectives really fast, especially with Bloodrazor and Rageblade, so consider dragons and heralds a higher priority when you are jungling on Yi.

His early game is fairly weak, but a well timed alpha strike can turn around early 1v1s. Yi really starts to come online later in the game especially when he has lots of items.

Avoid teamfights if you don't have defensive items, as you are vulnerable to CC and burst damage.

Yi can splitpush fairly well, but remember you only have your ult as an escape/engage. Engaging might be prefered as you can 1v1 or even 1v2.

Pathing (Standard) :
- Botside Buff (Ward are between raptors camp and river either on your side or enemy side depending on how strong your team is early game compared to enemy team). (This ward will help you spot enemy jg about a minute or a minute 15 seconds later.)
- Gromp (If started Blue). Wolves (If started Red). You can then look to clear raptors or gank before the scuttle spawns.
- Try to get the other scuttle if you can.
- Get whatever camp you can before you recall (at 900g).
- Continue clearing until level 6

At 6, Master Yi ganks will be much more effective and overextended bot/top laners will be easy kills.

Dragon: don't force dragons ever unless it's a dragon soul. Ward pit before you start it (obviously). 2nd or 3rd dragons will be easier to get as Master Yi.

Herald: Remember that Yi clears Heralds/Dragons/Barons really fast. Sneak it if you can.

Baron: prioritize Baron over other objectives in the mid-late game. Yi can sneak it but he probably won't be able to solo at 20 mins.

Yi is a fairly simple and straightforward champion, but he can also be easily punished because he lacks defensive tools.

Alpha Strike(Q) is Yi's signature skill and the most powerful engage/defensive tool. In the early game, use it to deal damage and chase a kill. In the late game, engage with Highlander and use Alpha only to dodge skillshots or chase if safe.

Mediate (W) is Yi's second defensive tool. Yi takes reduced damage while meditating so you can use it to stall a fight while you wait for reinforcements, or to tank towershots after a tower dive. Yi's healing is increased based on missing health.
Meditate can also be used to reset your aa timer. (pressing w twice quickly)

Meditate Bug: Not sure if it still works, but pressing w twice quickly will also let you tank a lot of tower damage.

Wuju Style (E) lets Yi deal bonus true damage on hit. Save it for duels/skirmishes/teamfights. It also helps early clearing.

Highlander(R):

Passive: Takedowns reduce cooldowns of Master Yi's basic abilities by 70%. If you get a kill, your alpha and meditate cd is reduced.(your defensive tools). Consider this when you are teamfighting or skirmishing.

Active: Yi gains bonus movement speed, attack speed, is ghosted and immune to slows and cripples. Takedowns extend active by seven seconds. Highlander timer is paused during meditate.