How does one get better at real analysis proofs? How does one proceed through a math proof in real analysis? My instructor always says make a diagram, but I am not a visual learner. It seems that whenever I write out the definition of an assumption, then I cannot make the next logical step. Also, when I go to try to verify that my proof is correct, I ask myself questions like, "why must this be true?" but the proof does not end up not being air tight. For those that have had real analysis, what did you do to master proofs and do the exercises? 

I think the best thing to do is to learn and understand the proofs of the theorem you do in class. The key thing about analysis (as opposed to algebra) is that all the proofs have a pattern to them.
For example: The proof of sequence of continuous functions converges uniformly to a continuous function uses the idea called $\frac{\epsilon}{3}$ argument. By knowing this technique, you can do a number of other proof that involves convergence and continuity.
