This is a really terrific book & worth every penny!
Observing Variable Stars: A Guide for the Beginner, by David Levy.
I have it and David Levy explains things so well with such enthusiasm- an easy read/guide.
A good one to start out with I guess would be Algol- The Demon Star.
It's a bright star looking north in the constellation of Perseus, easily visible to the naked eye. It's brightness changes every 2 days. Apparently you can observe these changes during the course of an entire night's observing.

Wait a few months for the constellation to be in our skies again.
http://en.wikipedia.org/wiki/Algol Keep scrolling down & check out the animation!
In 2011, the star Mira was an awesome site to see. All of a sudden there was a bright orange star in the constellation of Cetus. It was so much fun watching it slowly fade.
http://www.skyandtelescope.com/obser...130722493.html
And read here:
http://www.oneminuteastronomer.com/2...onderful-star/
I'm not an expert here in variable star observing- I've not actually done it yet in any serious way, but someday I hope to.
Does anyone know when Mira will get so bright again?