Forget means I do not remember
Forgot means I did not remember (and now you do)
So let's say you missed an appointment you had yesterday with your friend. Telephone rings, friend asks: Hey buddy where were you? Answer: Shoot I forgot (and not shoot I forget)
Now let's say you have an appointment but can't remember when. You call your friend and ask,
Sorry, I forget when our appointment is, do you remember?
and not: Sorry, I forgot when our appointment is.
To expand, lets say in the last example your friend responds: You dummy, it was yesterday.
You reply: Sorry, I forgot (not Sorry, I forget).