Math question about set theory

Can someone please help thanks.
How to prove that one set is a subset of another?
And how to prove that two sets are equal?

I will introduce letters.

To prove that set A is a subset of set B
you prove that each element of A satisifies the conditions for
being in set B

To prove that two sets are equal, you do this twice.

You prove that A is a subset of B and that B is a subset of A

IF both of these are true, then A and B MUST be the same set.