As an Irelia main, I can tell you it's a very equal skill match up. (I do agree that riven is kinda stupid though. No resource bar, AOE execute ult, 100% AD shield on 4 second cool down later on, etc.) but that's just my opinion.
Try starting cloth 5 into ninja tabi. From there, either start sheen for trinity if you have the money for it, or start building into blade.
You could also experiment with building cloth into thornmail, while building blade at the same time. It's worked for me quite a bit in the past. but take into account the enemy's team comp when doing this; building thornmail when they have 3 other ap's on their team might not be the best thing to do. When doing this, I recommend getting 2 daggers first, rather than building builgwater (Assuming you're maxing W first) If you see she's starting brutalizer, which is very likely, consider holding off on armor, and just rushing your first damage item.
Unless the opportunity presents itself, don't fight riven before you hit 6. If she engages first, hold out on activating hiten style unil after she uses her knock up, as that mitigates alot of potential damage you could get off on her. Save your Q for later in the fight just in case she tries to run off if she feels she's losing the trade. Other than that, try to play passively and farm with your Q.
Eventually, assuming neither of you have died, you'll over power her very easily. Just be extremely careful: If riven gets even one kill on you early, it'll be almost impossible to recover. (Visa versa, if you get a kill early on, it'll be hard for her to come back. 2 kills early on basically
tee's your lane dominance, but most Riven players aren't sloppy enough to allow that.
Of course, if you decide to go sheen, try and space out your skills. E first, and auto. Holding off on activating W(Which is a good idea when facing her as mentioned above) will get you another proc, and spacing out your ult will get you 4 more procs (In a perfect scenario. In reality, you might get 2, or 3 if you're lucky). Above all, {I'm guilty of this at times} get baited into fighting her if the starting items you chose were meant for more passive play. I.E trying to fight her when you started flask, or even cloth 5, and she started Dblade. (Cloth 5 less so, but definitely not flask). Unless she really fucks up, you will die, and it'll be a nightmare from there.
To secure your win, buy a skin, and believe In the power of Irelia
#PraiseIrelia 