I had started with Rosen, but early on found it a bit abstract. Over a period I have got comfortable solving problems in that text.
But, the one book which helped me with a good understanding and basic exercises was this book: http://www.amazon.com/Discrete-Mathematics-Applications-Susanna-Epp/dp/0534359450/ref=sr_1_5?s=books&ie=UTF8&qid=1304110580&sr=1-5
I really loved this book and it helped me ease into Rosen's text after one semester.