My opinion of number theory is a lot like Paul Graham's opinion of philosophy: the best way to learn about it is by studying other areas of mathematics. Number theorists actually have very little vocabulary and very few proof techniques that aren't borrowed from other areas of mathematics. I suggest simply reading the following wikipedia articles, in roughly this order:

Group (mathematics)
Ring (mathematics)
Integral domain
Fermat's little theorem
Euler's totient theorem
Chinese remainder theorem
Bertrand's postulate
Prime number theorem
RSA
Diffie-Hellman key exchange

http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html