This classic text is well rendered on the link given. One cannot overestimate its historical importance - even Isaac Newton wrote his works in 'Elementary' fashion: http://members.tripod.com/~gravitee/toc.htm" [Broken]. The Elements of Euclid are not difficult, but they do give you a taste of what mathematical proof entails. Once you get the feel of how an axiomatic system works, you can venture into more difficult texts that bring into relief the various methods.
For more modern texts, there are quite a few specialities - are you interested in logic, boolean algebra, set theory, number theory? The reason being is that many of these disciplines have their own methods, though all of them of course are analogous. If you are more interested in the philosophical aspects, of course there are other texts. The reason I ask is that it can be a little dry just reading 'how to prove something' without being interested in whether it is true or not.
I would simply read the classic works first - even the ancients, as they are classics for a reason - and then venture into deeper waters according to your interest.
The ability to prove something is perhaps the most seductive thing about mathematics - and some of the greatest mathematicians (such as Gauss) would prove some theorems in many different ways (as in the case of the Quadratic Residue theorem)!
In any case, good luck !
PS> on a humorous note, I found this http://paul.merton.ox.ac.uk/science/maths-proofs.html" [Broken]