Do you know how to find determinants? There isn't really anything fancy to understand, the cross product is just a defintion.

If "a" and "b" are the vectors:

The cross-product is the vector defined by:

This is difficult to remember, it's best if you know how to find determinants.

http://en.wikipedia.org/wiki/Cross_product

If you scroll down to "matrix" notation, you'll see how the determinant definition makes 3-by-3 cross products a little easier to remember.