It's been a while since I've done these, but I think I can help you.
There are two ways to do it: you can go straight to the diagram or you can try to optimize the function and get a solution that uses less logic gates to do the same thing.
1: Direct
You check the truth table to see where the output is 1, you get the corresponding function and then you build the circuit.
In your example, the output is 1 when (A=0 AND B=0 AND C=1) OR (A=0 AND B=1 AND C=0) OR (the rest...).
Basically, X = A.B.C + A.B.C + A.B.C
(Underscores should be overscores)
Then you just draw the circuit.
2: Optimize
You use Karnaugh Maps.
I googled this site: http://www.maxmon.com/kmaps1.htm
I only scanned through it(i.e. looked at the pictures...), but it seems to provide a reasonable explanation.
In your example, you would get something like this:
AB 00 01 11 10
C 0 0 1 0 1
- 1 1 0 0 0
(this map is a little crooked, but you get the point...)
Then you link the 1's in 2^n groups (1, 2, 4, 8...) and get the corresponding function (check the site).
Which in this case is pretty useless, since you get the exact same function.
Karnaugh Maps are very useful in more complicated functions, though.
There is a third option left: you do what YT2095 said, and notice that the function is a triple input XOR. But you said you "think it SHOULD be used with AND OR and NOT gates combined", so use the first option.
If you want to learn more about this (or if you are forced to, like I was...), you can check this book, which I used last semester to learn this:
Morris Mano e Kime: Logic and Computer Design Fundamentals; Prentice Hall
It's very good, but also expensive. I remember I found the book in a online version a few months ago... google for it.
I hope this helped, but I may have said it all wrong. I didn't pay much attention to this stuff last semester.
Edit: got the underscores in the wrong place...
