Personally, I am not of the school of thought which says that every reader needs to independently verify every theorem. If you are just beginning to work with proofs, you should read all of them, but you do not necessarily need to work out every proof in all of its detail yourself.
However, I think it's a good idea to pause between reading the statement of a theorem and its proof to consider yourself what a proof may involve. Ideally you would prove it yourself, but this may be difficult and it's not always worth your time. At the very least, you should ask yourself the questions:
1) Is the theorem plausible? Does it match my intuitions? If not, what is going wrong? Try to construct a counterexample.
2) Is the theorem interesting? Why did the author choose to state it? Is it a "technical" lemma, uninteresting in itself but perhaps useful later? If so, it might be wise to postpone reading the proof until you understand why the statement is useful.
3) Is there a clear connection between the hypothesis and the conclusion - that is, do they involve similar-sounding definitions? If so, it's probably an indication that the proof is straightforward. On the other hand, if there seems to be a yawning gulf between the hypothesis and the conclusion, this might be an indication that some "high-powered" theorems are necessary to proceed. Can you identify which ones are necessary?
4) What is the central difficulty of the problem? Often when you first read a proof there is some niggling doubt in the back of your mind - some confusion that you can't put your finger on. Try to pinpoint this confusion by putting in the form of a question that is as specific as possible. "How on earth could I get $X$ only knowing $Y$?" "Doesn't this violate Thoerem 8.7?" "Isn't this trivial because of $Z$?" This sort of frustration is a good sign. It's much, much preferable to a general haze and confusion - having no idea what the author is trying to do and why it's relevant. Try to hold onto these questions - don't let them pass until you have your answer.
The point of all this thinking in-between the reading of the statement of a theorem and its proof is to get the largest possible "ah-hah!" moment when you read the proof. Then when you think about the problem later, you will remember the "ah-hah!" moment even when you've forgotten the other details. If you can remember the clever part of the proof, you can reconstruct the other details later when you want to.