From my initial comment:
Take a look at Velleman's **_How to Prove It: A Structured Approach._** It covers proofs using a variety of methods, including proofs by induction, and covers basic logic early on.
You might also want to take a look at Rosen's **_Discrete Mathematics and Its Applications_**. It's great for an overview of Discrete Mathematics. Between this text and Velleman's text, you'll learn most of what you need to know or to reference.