The easiest way is to check all the vertices of one polygon to see if they lie inside the other polygon using the contains( x, y ) method.
However, this method is slow O( n * m ), where poly1 has n vertices and poly2 has m vertices, and can give an incorrect result ( think about two triangles in a star of David type formation ).
The more complex way is use a sweep-line strategy to check if any of the polygon edges intersect. This method will find all cases of polygon intersection and runs in O( p * log p ) , where p = n + m.
If you google for "line intersection" and "sweep line" something may turn up. It is also detailed in "Introduction to Algorithms" by three guys whos names i can't remember???, but their initials were C, L and R
If you don't find anything, come back here and I'll put up an explanation about how it works when i have more time.
