At it's simplest, you could use AABB (Axis Aligned Bounding Box) collision detection.
So for example, you could define a rectangle object for each 'thing' in the world which needs to be able to collide. That rectangle would need to be updated when the graphic transforms (eg scales / rotates / moves).
AABB collision detection is quite fast and simple, and will resolve to give you a vector which represents the intersection between the two collision shapes (direction and magnitude), which you can handle however you want.
This is probably the best tutorial on AABB i know, note that I don't think the example code supplied is very useful for learning though (written in as2 as i recall, and organised in an fla timeline, a mess for trying to look through)
Of course, this is all with rectangles, and if you need more advanced collision detection, maybe look at the opensource as3 collision library implementations eg box2d or nape, which i think theres a lot of talk about even on this forum (i ave no experience with either really, but I think its possible to create custom collision shapes).
SO, sorry if my answer isn't that helpful! but this is the kind of seperation of art / physics simulation that Henke meant