Archaeology is a fascinating discipline, and I'm glad you've decided to explore it! There's a lot more to archaeology than meets the eye - a lot more than digging around until you find something cool. Archaeology requires caution, precision, documentation, and careful analysis. It's a lot of detective work - definitely for puzzle-solvers! But if you can stand the detail work, you'll find that it's a lot of fun. There's nothing quite like holding something in your hands that no person has touched in 2,000 years!
Here are two of the newest, as well as one of the old standards (Martha J's book, which is an oldie but a goodie). Note that these are not cheap because the market for books on archaeology isn't a huge one. If you're interested, I'd recommend seeing if you can check them out through interlibrary loan. If you want to buy, and if money is a concern, check out used versions on Amazon.com. Also note that there really aren't scholarly books on archaeology written from a Christian perspective.
Fagan, Brian. Archaeology: A Brief Introduction (2005)
The most recent on the market, and it does consider archaeology as a career.
Joukowsky, Martha. A Complete Manual of Field Archaeology (1980)
This is the standard "how to" book. It can get pretty technical, but it covers everything.
Renfrew, Colin. Archaeology: Theories, Methods, and Practice, Fourth Edition (2004)
Not a cheap book, but a nice one, and Colin Renfrew has become one of the biggies in the field now.
A couple of these are very recent and have good bibliographies to lead you to other works. Also note that there are a number of books on specific topics, like archaeological photography, archaeological illustration, aerial photography, etc.