Here are some examples:
No comma needed:
* I like apples and oranges.
* She went to the store and bought groceries.
Comma needed:
* I went to the park, and I saw a dog playing fetch.
In this case, "I went to the park" and "I saw a dog playing fetch" are both complete sentences, so a comma is necessary before "and" to separate them.
Let me know if you have any other questions!