I wasn't thinking of any particular book. There are many called "Introduction to xxx", and replace xxx with "Number Theory" or "Graph Theory" and you're likely to have a good book in your hands. There's a brilliant book by Hardy & Wright, but it may be a bit fast paced for a truly first introduction. There's a recent book by a friend of mine: https://www.amazon.com/Proof-Mathematics-Joel-David-Hamkins/dp/0262539799 that I've read and love. It talks about how to find and write proofs.
I haven't read this book (since it's not available yet), but it looks promising:
https://www.amazon.com/Proof-Mathematics-Joel-David-Hamkins/dp/0262539799