Because deductions in logic may remind you of math, you might expect them to be as hard as math problems. Absolutely false. Math problems and proofs call for intuitions about numbers and space that some people find more challenging than others. The great advantage of proofs in logic is that they depend only on intuitions about what makes sense; and every human adult already has these intuitions. Logic only makes them explicit.

There is no mystery about going forward with a proof when you have a strategy already in mind. But what if you don't? What if the premises and the desired conclusion sit there on the page, daring you to put them together, and you don't know where to begin?

Two things help at this point. They should not be taken as rules or strategies for logic, but as approaches that anyone can take when stuck.

1. Look for elements in the premises that are identical to, or remind you of, elements in the desired conclusion. If (C & D) is part of the conclusion and appears in one of the premises, start with that premise.
2. When all else fails, begin with the premises and do whatever you know how to do with them. If one premise is ~(A & B), use DeMorgan's Law to translate it into ~A v ~B. Will this help? It can't hurt. And it's likely that, after you have translated all the individual premises into other forms, something will spring to your eye. In the same spirit, if two premises seem to work together, derive their conclusion. For instance, if one premise is (B v C) → D, and another one is ~D, you know that together they produce ~(B v C), which becomes ~B & ~C. Will this help? Look at the other premises, and at the conclusion again, to see.

Finally, don't get discouraged. There are a finite number of things you can do to your premises, and to the consequences of your premises. Eventually, if the argument is valid, you will reach the conclusion.

This, by the way, is a known fact. Every valid argument in propositional logic can be proved to be valid. (This is what the system's completeness amounts to.) Another way of putting this is that a computer can be programmed to start with premises and reach a desired conclusion, if the argument is valid. The computer might be sloppy about it, trying every move in the book to get to its conclusion. But eventually the computer will reach its answer. Therefore you will too. And you will learn from experience. You will find that as you do more proofs, you will make fewer and fewer wrong moves, until doing proofs is as natural to you as tying your shoes (remember how hard that was!).

The point of mentioning computers is that programming them to do proofs is not particularly hard. Nothing about these proofs requires special insight. Again: Logic is not like math.