This is my build for a hybrid Yi. You have AP and CDR for Alpha Strike and then an active that deals AP, from Hextech Gunblade, making you a solid force of AP. Then, you have AD from Berserker's Greaves, Youmuu's Ghostblade, Hextech Gunblade, and Lich Bane's passive, making you also a solid force of AD.

Very heavy on the attack tree. Just doing tons of damage is your role pretty much, so this fits him well. I like going in to the defensive tree next. Anyone can benefit from some extra armor and magic resistance. It isn't worth getting the health and mana regeneration masteries, in my opinion, since your W and life steal already regenerate a lot more health than that will and you have clarity for all the mana you should need.

Armor Penetration Quints and Marks - So you can kill faster, especially early game.

CDR Glyphs - More ability spamage ftw. This is especially good for lots of Q,W and then it allows you to have your ult for pretty much every fight.

Dodge Seals - So you can live longer. These are especially needed since you're a melee without any armor items.

Lots of Q,W. With Clarity, you'll be able to camp around in lane pretty much forever. You'll also get lots of farm with Q and your health bar should pretty much always be close to full from your W. E is a solid ability too, but it really doesn't fit with an ability-spam Yi that goes Clarity, so I don't get it until level thirteen.

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Teleport so you can backdoor, spend less time in your base, get to team fights faster, etc. It's a great spell for all game really. During early game, it allows you to go back and then return to your lane in a few seconds. It can also be used to teleport to a ward and then gank. Then, during late game, it allows you to get to team fights and backdoor. You should make sure that your team (and yourself) is using wards, since that's the best way to utilize teleport.

Get clarity so you can almost-constantly spam your abilities. Clarity also benefits the rest of your team, though not much since you aren't getting the Clarity mastery. Along with your CDR items, this will give you lots more Q,W spam. This makes you harder to kill and allows you deal much more magic damage, making you a viable hybrid. It also makes it so that you don't have to build any mana items, which would set back your build.

Doran's Ring is a great first item on Yi. The health, ability power, and mana regen all benefits him greatly. Another option would be boots or a mana crystal and potions. Ability power is great on Yi, since it allows his W to heal for more. Thus, ability power functions basically the same as health pots, allowing you to heal for more. As long as you have mana regen, you shouldn't need any pots or anything at all, making this the best start.

I prefer Berserker's Greaves for extra damage. Other good options include Mercury's Treads for tenacity (which can be great in some games) and magic resistance, Ninja Tabi for dodge and armor, and Boots of Swiftness if you just want to be able to run faster.

- Sheen is a great item for Yi, especially early in the game. Ability power and mana are both great for him and the passive is great combined with Alpha Strike.

- Youmuu's is another very good item for him. Everything about it is just really good. Its active is especially good for going for kills and may be used to retreat faster, if need be.

- Gunblade is a very good hybrid item. The best part of this item is the life steal, but everything else is very good as well. The active is especially good for an extra slow, since you don't have cc. You need this item or at least a Vampric Scepter somewhat early in the game, so you can last longer in fights.

- This is a great item for hybrids. It has CDR to max you out at 40% and then has some ability power and attack speed. You could also get a Deathfire Grasp or a Morello's Evil Tome, but I prefer Nashor's for attack speed.

- The item is best for its passive, which goes great with your Q and E and, unlike the Sheen, it can be used many times in a fight. I wouldn't get this early, since its passive goes with AP instead of doubling your damage, so it's best after you have other AP items. Then, the movement speed, magic resistance, and ability power are all very helpful as well.

Here are some options for your final item in the build.

- Frozen Mallet is a great item. The slow makes you a much better chaser, since you won't have to run as far, and the health is also very good, especially against high-burst champions or when you're being focused hard.

- Everything about this item is very good. It has both damage and attack speed, making your AD a lot stronger. Then, it also has a magic-damage-per-hit passive, which is great since you have a lot of attack speed with this build. This magic damage will also make your spell vamp from the Gunblade more useful.

- Banshee's Veil is great, since it gives you a little health, magic resistance, and then a great CC block. Get this against teams with annoying stuns.

- This is a great item for just making you last longer in fights. The passive is especially good. Get this just when you're having trouble staying alive in fights.

- A second Gunblade can always be good, especially if you're fed. It will make you kill faster and stay alive longer. This is a good item for when you're fed and want to be able to win fights, basically, on your own or with little help.

- This is a great item that gives you a little of everything. It does lean to the AD side though. It's probably best for its speed buff and health. This is arguably a better item than the Frozen Mallet.

You can go top, middle, or bottom. You could even jungle if you want. AP Yi has the ability to last forever just about anywhere with just about any match up, while still getting solid farm. He's also very hard to gank, since his ult is pretty much a free get away button and his W allows him to keep his health high. I would say he's best in solo lane, especially since, while duo laning, he just tends to steal minions from whoever he's laning with. He's also typically not best at middle. High burst AP champs generally own the middle, since they can kill a lot easier while still farming.

Farm with your Q, heal with your W.

You're supposed to farm with your Q, but that doesn't mean you should push with it. Normally, especially early on, you should primarily last hit to farm. Then, whenever your lane is being pushed back, you can use it more. However, as it levels up and you get wards, you can start to get away with using it more.

When using your W, it's important to note that you should be close enough to continue gaining experience from minions slain. This is important to make sure you don't lose level. However, if you can't safely do this or if it will only make the difference of one or two minions anyway, you may retreat further and then use it. Do not use it where the opponents can easily hit you though. It does grant you extra armor and magic resistance, but it's better to take no damage than to take a little.

In team fights, you basically use ult, alpha in, use your item actives, fight until you're low, retreat, use W, and alpha back in. Since you're squishy, you should always wait until at least one or two of your team mates has already initiated the fight and then go. This won't slow you down much anyway, since your alpha allows you to instantly join a fight from a ways away.

Master Yi is possibly the best backdooring champion in the game. In fact, he almost definitely is the best. You aren't building AD here, so you'll be a bit slower, but you definitely still can backdoor very effectively. One of the main reasons I get Teleport as a spell is for the sake of backdooring. It allows you to get to a turret with your minions nearby in an instant, so you can snipe the turret. However, it's best used when you have wards near the enemy's turrets. That way, you can teleport to a turret that seems completely unthreatened to the other team, so they won't be guarding it at all.

Pros-
You have two slows, one is an an-hit slow.
You're much harder to kill.
You have very high burst damage from item actives and alpha+lich bane.
You're harder to counter by either armor or magic resistance.

Cons-
You deal less total damage.
You aren't as great of a backdoorer.
You don't run as fast (assuming you would get at least one phantom dancer).