Ok, here's what you do:
So the team fight is about to start, both teams are hovering near each other. Ideally, you are in another lane farming/pushing. As soon as you wipe the current enemy creep wave out, head towards the fight. Make sure theres no creeps left so no enemies that are paying attention can know for sure you're coming. Hover out of range watching the battle. Do NOT join in to the battle itself. As soon as their squishiest player (prolly a mage, possibly a carry) is around ~50% hp, alpha strike to him. the instant alpha strike ends, you'll be next to him (assuming {LULZ} that you didn't kill him already.) As soon as you land, activate wuju and highlander and right click that enemy. He should die almost immediately. And your cooldowns get refreshed. Alpha strike to next squishiest. Rinse and repeat till GG.
Alternately, when the team fight starts, start blowing through your mana to push a different lane into their base. <-This is what most guides/Yi players will tell you to do. Really depends on the situation, location, players, and champions.
As far as not dying: ignore every other guide out there, and start off with a regrowth pendant and a health (or mana if you want, but you shouldn't need it) potion. If the enemies are focusing you even a little bit, being aggressive, ganking you, etc., build warmogs. Just do it, you'll thank me. Otherwise, sell it later when you don't need it.