Step by step for you mate =)
Champion select:
(yes annie can play any lane)
If played safe, these will come out on top. Also, if its Riven top build full AD garen- it pays off far more.
Gameplay: Let riven push, overextending will result in heavy and possibly fatal damage. The trick is to freeze lane in front of your tower (not under it) so that your jungler can consistently gank AND your minions are sitting under tower range making it so that she has to take damage to get cs. This takes practice, and with new reworked Fiora I too am having some difficulty properly freezing lane. If you can't freeze lane, let Riven engage you in your wave and then cc her within it so that she takes hefty damage from minions and you. The only one who does not care worth a @#$@ about pushing is Kayle. She autopushes and will inflict damage on Riven, meanwhile Irelia will full counter her so Irelia can just freeze in lane and outrade consistently (mild sidetrack). Now that laning is over (one or another tower is taken, contesting dragon) get with your team. If you managed to freeze your minion wave well, you should have a high cs lead on Riven and if she didn't manage to roam successfully she should have pretty minimal damage. Use your cc (or mega damage vlad/yorick can just push all day) to lockdown the most fed player on the enemy team-if Riven did get fed somehow, your job now is to make sure that if she comes looking to engage that you will beat the stuffing out of her before she can hit your team.** Basically you want to send a message- you are riven's opponent, you are the threat, she needs to focus on you.**
Itemwise: Thornmail (before you hate) hurts her for using her passive and is also the most gold efficient armor item. If you are still having trouble grab Frozen Heart- Omen will do absolutely nothing against Riven because she uses her spells not move speed. Never build full tank, always build at least one damage item. Item's vary from champ to champ of course, but for the majority of the ones I listed these work.
Personal Suggestion: Take Annie, Garen, or Cho'gath top. Annie can farm safely and punish the @#$@ out of Riven for overextending, she'd my go to if I were you. Second place is Garen because he has a silence, and a silenced riven is a dead one- also building full ad Garen means you will HEAVILY outrade her every time you manage to silence and then sit in the minion wave. Cho'gath is equally powerful as annie, but its on the note of his sustain- killing minions heals him, and he has an aoe silence/knockup which will make Riven question the idea of coming into your domain.
Hope I helped =) Any questions feel free to ask, I tried to generalize this a bit.