As Hellfire says, if you simply think of sprites as rectangles then you can test the points (corners) of one rectangle to see if they lie inside the area of the other one and if any of the corners lie inside then you could say that you have a collision.
This is a pretty fast way of doing things and in a quick paced game nobody would notice it is not 100% perfect.
If you want 100% accurate collisions then you need to use another technique which would involve creating something called bit masks for your sprites, these are slower, to impliment them quickly is a little bit out of your range at the moment so I'll make a deal with you, if you code the basic collision of rectangles overlapping to show your progress then I will change that code so that it uses image masking.
