The issue is whether and is joining a compound verb or a compound sentence. There should not be a comma before and when it joins a compound verb:
Alice picked up one of the books and read it.
Usually a comma should be used before and when it joins a compound sentence:
Alice picked up one of the books, and then she walked out the door with it.
You may use the clue that a noun or pronoun follows and, signalling the start of a second clause (which is what makes the sentence a compound one).
The comma may be omitted, however, if the thoughts of the two clauses are closely related:
Alice picked up one of the books and she dropped it immediately.