I play Yi a lot in pubs, and basically there's always a moment when Yi is ready to start ganking. It just... clicks. Usually, it's when I wind up doublekilling the enemies with highlander and lifesteal items.
Early game, Yi's pretty easy to counter. Harrass ranged, try to make him flee. Personally, due to Yi's mana problems and the fact that Alpha Strike gets so many last hits, I never take meditation until later, just because I actually get more out of last hitting than being able to safely whack an enemy champion once or twice. Just harrass the Yi and try to make sure he doesn't get too many last hits (frequently, I get double or triple everybody elses, and that is a lot of gold).
Here are the things you need to do against a Yi lategame:
Get a freaking executioner's calling. This slaughters Yi, because he can otherwise take absurd risks, crit you for 600, and heal the damage of two other champions. Reducing his lifesteal by a ton makes him almost as squishy as if he had none.
Focus the **** out of him. Always hit the Yi. If you all focus, you can generally kill a Yi off without letting him get a kill, or maybe only one if you don't have any hard stuns.
Never, EVER burn a stun on a yi you can't kill. Just don't do it. If you do, then he'll retreat, heal, and come back, while your stun is on cooldown (well, unless the stun recharges fast, in which case it's probably fine to harrass).
Never use any skill that brings Yi into melee range, ever, unless you have a lot of backup. For example, Amumu. If you bandage me and go into your ultimate, you *might* hurt me a bit, but, since you are a tank, you're going to get lifestolen so much it doesn't matter, and your 3% damage aura doesn't do much with my low base health. Tristana hitting Yi with rocket jump is another dumb move, because it doesn't slow me, but does let me kill you.
If Yi has a banshees veil, burn a slow on it, since those fail anyway. No sense wasting stuns on a Yi who's immune to one.
Be careful of Yi's who have a spellshield up, because... well, that's just cruel to the enemies if they don't have a lot of moves to waste on Yi.