It depends on what she brings during the laning phase. If she gets a flask and some pots, she's there to stay. Don't bother trying to win trades (don't let her push you around, tho), so play safe. Irelia has a somewhat weak early game until she buys triforce (or gets a kill).
One way to beat her in a trade is to use slows when you know her W is active and poke her (if you have range) or wait until it goes on cooldown to engage. She can also be bursted down early (pokes won't work against sustain, you have to burst) if you stun her, so get your jungler to gank. Your jungler should be ganking top early against Irelia, because that's an easy first blood (flask doesn't mean much when you're stunned and two champions are wailing on you, flask doesn't give extra stats after all).
Irelia is very aa reliant, so thornmail is an excellent options. A little health works, since her true damage isn't too much compared to Vayne's so build stuff like randuin's omen or warmogs. Hell, even sunfire's cape would work if you're melee and need to get in close.
Being aa reliant, Irelia doesn't have as much utility in a teamfight, so position properly and don't let her get to your squishy adc.
One last tip: If you're low on health, or you're about to get Irelia low on health so you can go HAM, then stay away from your own minions. One trick I've learned playing as Irelia is that Irelia can have massive mobility that would make Lee Sin cry if she's by a wave of minions low on health due to her Q cooldown. Since it's situational and she has to last hit low minions to do so, there is a skillcap and price to this trick, so don't let her abuse it if she's actually skilled.
Also, if she hugs the wall on her side, she might have warded the camp with frog for a free escape. It's cheap, but I don't care if Lee Sin can ward hop and LB/Zed can do it for free.
already destroy her. For top lane, I recommend 
or any tank, my favorites are 
.
also work.
