Sample Full Build
Riven requires practice. Learn all her auto-cancels. Learn her animation cancels (eg E cancels initial ult animation). Kill people.
Riven is a fighter. She's not quite an assassin, although she can play like one, and she's not quite an off-tank, although her E and CC can make it seem like she is. She's very high damage, very mobile, and very snowbally, in both directions.
Can take Ignite or Exhaust, particularly if you opt to play her Mid. Don't recommend in most cases.
Riven's build path is pretty flexible. It pretty much just needs to meet the following criteria. 40% CDR, sooner rather than later, Armor penetration appropriate to the situation, and lots of raw attack damage.
Ninja Tabi if they fight back with auto attacks, or if you don't need the other options.
Ionian Boots of Lucidity if you can crush them with early CDR.
Mercury's Treads if they can lock you down with CC.
For cooldown reduction:
You'll usually have 10% in runes. The other 30% comes from the following.
The Black Cleaver is never a bad item to have, and provides 20% CDR.
Youmuu's Ghostblade provides a lot of raw damage, and the active helps boost your already excessive mobility; 10% CDR.
Death's Dance is great for topping off your health, and provides substancial attack damage; 10% CDR.
Maw of Malmortius is your Death's Dance for magic heavy teams. Basically fills the same role, except instead of topping your health off, it'll mitigate magic burst; 10% CDR.
Edge of Night is a great damage item to have for killing carries, and the active will help prevent you from getting locked down while diving the enemy team.
Guardian Angel is the only full defense item I'd recommend on Riven, and only because the passive allows you to go all-in in game winning fights.
Mortal Reminder is your go-to tank buster, when The Black Cleaver doesn't seem to be enough. Also an excellent pick-up if you ever decide to forego The Black Cleaver for some reason.
Lord Dominik's Regards: Basically Mortal Reminder when they don't have forms of healing and sustain.
Ravenous Hydra: A great mid-game item for adding burst to your kit (4th item or so), as well as some lifesteal. If you want some sustain, and don't need the CDR from Death's Dance, it's not a bad option. Especially if you're split pushing.
Sterak's Gage is for mitigating burst, when it's not largely magic damage burst. Not an ideal item in most cases, but worth mentioning.
Mercurial Scimitar: Build this if you need a Quicksilver Sash to break suppression or specific CC combos.