Repetition
Have them read their lines out loud. Then repeat over and over again. Soon they will know the words by heart.

Make it fresh
Have them say it in a new way each time. Remember, when an actor delivers a monologue they need to make the audience believe this is the first time the character is saying these words. Have them discover something new each time they read it.

Roll the dice
Have them say the monologue while rolling some dice, or doing a puzzle, or making pancakes. Combing physical action with speech will help them remember the lines more clearly.

Talk it out
A good monologue sounds real, so talk to them about their character. What does their character want? Who are they talking to? What room are they in? The more the know about their character the better they will do.