Welcome to MHF Viperxxx10
I would love to help you with proofs
Since you haven't offered a specific example I will go through a sample problem and try to discuss my line of thinking:
Probably the most difficult part of proving something is where to start. It takes a lot of practice, and trial and error. This is what went through my mind as I solved the attached example.
"Well, I don't need to know anything about the lengths of the triangle, because all I've been given are angles. I remember that the sum of the angles of a triangle is always 180 degrees, but that doesn't help because I don't know what angle B is nor do I know what angle A is. Well, I know that angle D + angle C = 180. Aha! But I also know that angle D + B = 180, because together they form a straight line. So if angle D + angle C = 180 = angle B + angle C, then angle D + angle C = angle B + angle D, and once we subtract angle D from both sides of this equation, we get our result, angle B = angle C."
Notice that I tried to rule out some possible ways of proving the theorem, based on what I was given (and importantly, what I was not given). I then relied on previous theorems or things I already knew that were relevant. I applied what I was given in the problem to this previous knowledge, and I was able to determine that some of my ideas didn't work. Luckily, I recognized that I could apply one of my ideas to the solution, and at that point I was able to see that this was the right direction to take.
While this is not always how proofs are made the important thing to remember is to try to find out what information you can extract from the problem using your previous experience and theorems. As you saw above once I realized that I could use the fact that suplementary angles add to 180 degrees the rest was pretty simple. Your goal each time should be to find out what other lengths or angles you could find, and also which are impossible to find. Once you have recognized your possibilities you will be able to see your path to the end.