Both words are related to time. We tend to use 'still' to show that something continues to happen (or not happen when we are being negative).
I still haven't heard from him
I can't believe she still doesn't understand
I still love him
I can still speak French
We use 'yet' to show that something hasn't happened, but we expect it to.
Has he called yet?
She doesn't understand yet.
He doesn't love me, yet!
I'm not very good at French yet.
I think that's right. Hope it helps.