For any champion your build really depends on how you play. No one build will necessarily be the best. If you're playing Yi you should probably play pretty aggressively. It'd be best to build him items with crit chance and damage. I'd first build him a statik shiv personally (after tier 1 boots), then maybe either trinity force or blade of the ruined king depending on what you're wanting. Blade of the ruined king will give you more sustain because of the lifesteal. Another good item is a trinity force particularly because of the spellblade passive. It gives additional AD on his next attack after he uses an ability, and since Yi is all about hitting Q and staying on an enemy it's a strong item. Generally though you want to just build depending on the situation. If the enemy team has a lot of people building ability power, then something like a mercurial scimitar or hexdrinker/maw of malmorius may be useful for the magic resist. Or a guardian angel. But it's ideal to build Yi with a lot of attack speed and crit chance items. One of his passives is that his Q's cooldown gets reduced per basic attack I think. I would really recommend taking the time to read through all of his ability's and their passives as well as all of the items and their passives.
This is a good pure damage build.
http://www.mobafire.com/league-of-legends/build/double-strike-op-as-crit-237180
Though personally I'd get a shiv and frozen mallet rather than two phantom dancers, and a hydra rather than a bloodthirster.
Frozen mallet's good for the passive which slows enemies every time you hit them with a basic attack.
I wouldn't personally get Trinity force as an item for master yi, more of a leisure item if ahead and the main reason being that it costs a lot of gold. You are better off building a Bortk for extra sticking power.
Personally as a master yi main for a year (pre rework and post rework), i build him a glass cannon early and bruiser late; Rushing Youmuu's Ghostblade and Statikk Shiv as my core items, followed by Zerk's greaves, Infinity Edge, BotRK and a select few of defensive items such as Mercuiral Scepter against Hard CC and AP, Maw of Malmortius against Heavy AP, Warmog's for just 1000hp, Frozen Mallet if your enemies have plenty of escapes, Randuins omen if the enemy is heavy AD and you want extra sticky power or a good ol' Guardians Angel if you keep getting focused.
Oh and if the game drags out for so long, sell your boots and pick up a zehpyr for dem stats yo.