STILL- 1. means that there is no sound or movement 2. on going or continuing
3. still can replace words like but or however.
Example:
I like Charlotte, still she makes me nervous

YET- 1. at a future time  2. at the present time 3. like still it can replace words like but
or nevertheless.

Rules of Thumb
1. Use still when there is a period of time covered.
Example: He started when he was five and he still wets his bed. (from then up to now)
2. Use yet when it refers to an instant in time.
Example: The bomb hasn't exploded yet!
3. If still is used at the end of a sentence it refers to quiet or lack of noise, in any
other case you must use yet. Perhaps this reduces ambiguity.
Example:
The morning was still. The morning is not over yet.
4. Generally, yet is used after a verb and still before it
Example: I still don't like you. They haven't yet fallen in love.