How do I improve my riven skills?

Make sure you mash your keyboard harder kappa

Learn the combos and animation canceling. It would take a lot of practice, unless you're okay with sticking with silver level combos lol

Play a lot of Riven

Make sure you last hit well. Practice being more aggressive - don't be afraid to die and lose lane, the only way you'll learn to succeed is to fail. Watch Riven streamers (BoxBox and Dekar are my recommendations).

In a general sense - know when to use which ability. A classic example is vs Jax. Against him, his power comes through his counter strike being able to negate a lot of your damage and then returning it. A tip vs him would be to save your stun purely for when he activates his counter strike. Then walk, dash or Q away and then return a combo of Q's after his counter strike has ended. Try your best to bait him into an all-in and stun him during his counter strike. THEN go all in when you have your cooldowns.

This can be applied to a lot of matchups. Riven has very low cooldowns, so if you can bait someone into an all-in where they spam their abilities, back off and then go ham onto them when you have your abilities back. If you are against nasus, Q into him and the moment you see him charge his Q, use your shield to negate a lot of the damage and then finish off you combo and back off.

And so on, and so forth.