Riven is strong in 3s due to her strong early game, high mobility, and high damage potential. Riven is good at both jungling and top lane. She can win most matchups top lane pretty easily. The only ones to watch out for are Jayce, Jax, and Garen. These aren't direct counters, and you can still do fine against them, but they are particularly good against Riven. In the jungle, she is also effective. Her clear isn't the fastest, but it is decent. Her level 2 gank is pretty good. Riven can cut people the bottom laner off after grabbing the health relic and usually get first blood.

Jungle and Top lane have very similar builds. Riven serves the same purpose in these roles, she just gets her farm from different places.

Boots- I get either merc treads or ninja tabi depending on where most of the damage is coming from. If they have mostly AD and not very many stuns, ninja tabi is better. I usually get merc treads because MR is hard to find on other items and the tenacity helps a lot against stuns. I don't buy the CDR boots because they don't give any defensive stats.

Black Cleaver- Key item on Riven because it gives AD, HP, CDR, ARpen. All these stats are needed on Riven.
Ravenous Hydra- This item increases Riven's damage by a ton. The AoE damage increase stacks with Riven's passive to deal melt people. The regen and lifesteal also help with sustain.
Frozen Mallet- I usually get frozen mallet next for its high HP. It helps me stay alive through team fights. It also helps chase people down.
Maw of Malmortius- There are limited options for Magic Resist on an AD champion. Maw has the best MR for still dealing damage. This is only necissary if they have significant magic damage, you can hold off on buying it if they don't.
Randuin's Omen- On twisted treeline, there is usually a lot of physical damage. All of your damage items won't do you any good if you die. You will do more damage the longer you stay alive. The armor and HP on this item makes it very potent.
Atma's Impaler- 3v3 games usually don't go on long enough to get a full build. The last item is pretty situational. I like to get Atma's for extra armor and it gives a lot of bonus damage due to the amount of HP in this build. It could easily be substituted for other tanky items such as Locket, Guardian Angel, or Banshees Veil.


Items not optimal for Riven
Sanguine Blade- I don't buy lifesteal because the map is so small that it is easy to just go back to base and heal. Tank items will keep you alive better in fights. Sustain isn't too important in TT.
Infinity Edge- Crit isn't the best on riven, and you need a bit of tankyness rather than full damage.

Pros
-Strong in lane
-Hard to Counter
-High Mobility
-Tons of Damage
-Can take some hits

Cons
-Gets kited be pesky ADC comps
-Hard to play from behind
-A bit on the squishy side

During the start of the game, it is very important to get level 2 before your opponent. Try to get in your top lane bush at the start of the game and have your teammates cover mid bush. That way, you can be sure that the bush is clear and that they don't gank you. You can safely start attacking minions to get a minion advantage on your opponent. Once you kill the second minion of the second wave, level an ability and attack your level one opponent. With Q and W and ignite, you might be able to pick up a kill, if not you will at least win the trade.

Level 6 is a huge power spike for Riven. With your ult, you get significantly more attack damage, and larger range. With the AoE of W and Q, Riven deals massive damage in team fights. The finish on her ult is also incredibly potent.

Riven can escape enemy ganks fairly easily with her high mobility. All you have to do is start running when you see the enemy jungler coming to gank. You should be able to outrun them with your Q and E. If you get caught you might be able to escape be stunning them (W) then flashing and Q E'ing away.

You can also gank bot lane pretty easily. If you push your lane to their tower, you can either steal their jungle, steal their capture point, or try to gank bot. Riven is especially good at ganking do to her stun and high mobility.