I could go into this answer, but honestly, it is such a broad and complex one. You are basically asking "How did Rome conquer the Mediterranean" and the answer to that is so much more complex than simply the army. If you're interested in the Army, I highly recommend Adrian Goldsworthy's The Complete Roman Army which will answer many of your questions.

This question is quite vague as it deals with a very long time frame and a very wide geographic area. There are many reasons for the expansion of the Roman Republic/Empire, not all of them military. I would suggest you look through the FAQ on the sidebar, some of the answers you seek may be found there.