How do actors memorize a script?

Some actors memorize lines by reading the script hundreds of times, others start off monotone and then add the emotion in later, others use cue cards, and so on. Additionally, actors have different background things they do to help them memorize better, such as exercising while learning lines.

Do actors read the whole script?

An actor will read a script once to understand the story, but most serious actors will read a script over and over and over to find those nuances, the themes, and the underlying message the writer is trying to convey.