We use yet with the present perfect tense to mean "up until now." Here are some examples:
A: Who are you inviting to your party?
B: I haven't decided yet.
I haven't finished my homework yet.
You don't need to drive too fast. The movie hasn't started yet. We have time.
We haven't seen the new class yet.
We use already with the present perfect tense to talk about something that has happened (or may have happened). It may have happened sooner than expected.
Examples:
I'm not hungry, I have already had lunch.
Father: You need to do your homework before you can watch TV.
Daughter: I already done my homework.
She has already watched that movie, but she wants to watch it again.
A: I'll do the dishes.
B: I have already done them. You can do the dishes tomorrow.