TITLE: how to be good at proving?
QUESTION [62 upvotes]: I'm starting my Discrete Math class, and I was taught proving techniques such as proof by contradiction, contrapositive proof, proof by construction, direct proof, equivalence proof etc.
I know how the proving system works and I can understand the sample proofs in my text to a sufficient extent. However, whenever I tried proving on my own, I got stuck, with no advancement of ideas in my head. How do you remedy this solution? Should i practise proving as much as possible? 
So far I've been googling proofs for my homework questions. But the final exam got proving questions (closed-book) so I need to come up with the proofs myself.
We mainly focus on proving questions related to number theory. Should I read up on number theory and get acquainted with the properties of integers? I don't know how I should go about becoming proficient in proving. Can you guys share your experience on overcoming such an obstacle? What kind of resources do you use for this purpose?
Thank you!

REPLY [6 votes]: Watch Suits, the USA Network TV series. They continuously say you should "press where it hurts", and that's the exact thing you do in mathematics. The border cases are always interesting, and the conditions for a theorem are almost always where a proof starts. For example:

A continuous function $f:\mathbb{R}\to\mathbb{R}$ which is negative at 0 and positive at 1 (that is, $f(0)<0$ and $f(1)>0$) has a zero somewhere between 0 and 1.

What you should use to prove this theorem is that the function is continuous, that it is negative at 0 and that it is positive at 1. Now, first think about what these things really tell you: what does it mean for a function to be continuous, and how can you use negative and positive? Why wouldn't the theorem hold for noncontinuous functions? Can you give a counterexample if the function is continuous, but positive at both 0 and 1?
Such questions give you hints as to the reason the theorem is true, and might just lead you to a proof.
NB: they actually said something along the lines of "press until it hurts" instead of "press where it hurts", but it is a nice series nonetheless.