logic
Let's say I have a truth table like this:
X Y A
t t f
t f t
f t t
f f f
Now, I have to find the formula for A. This case is rather easy because I can immediately see that this looks like the inverted values of X~B, thus ¬(X~B). Now, for a more complicated problem I do not know the method.
X Y Z A
t t t f
t t f f
t f t t
t f f f
f t t f
f t f f
f f t t
f f f f
Is there an approach i'm missing here?
Layout: You want the first line to be true when $H,M$ and $B$ are all true. So your statement $F$ must look like $(H\land M\land B)\lor \text{Something}$.
But you also want it to be true when $H,M$ are true and $B$ is false, equivalently, when $H, M$ and $\neg B$ is true. So, using the information in the paragraph above, $F$ must look like $(H\land M\land B)\lor (H\land M\land \neg B)\lor \text{Something else}$.
Proceed in this fashion to find $F$.
Edit: Firstly note that we need only apply this technique for the true lines, because by exactly pinpointing the true lines, the falsehoods will be determined.
So inspecting the true lines you can find:
$$(H\land M\land B)\lor (H\land M\land \neg B)\lor (H\land \neg M\land B)\lor (\neg H\land M\land B),$$
which has the expected truth table: 
Best Answer
I believe Karnaugh Maps are useful for this purpose.