Collision Detection and Collision Response

I've been trying my hand at representing a few moving/rotating objects using androids Opengl. Now I'd like to allow them to collide and respond realistically.

Researching the issue, I can find many resources that advise me on ways to determine whether two 3d shapes are colliding in the current frame (or whether they'll be colliding in the next frame). However, I'm having trouble finding resources describing how to get information about the collision that has occurred.

For example, using convex shapes, I would want to know which vertex collided with which plane first, at what time in between the frame. This way I can know how each shape should respond in its position and rotation.

I can describe the motion of each vertex with a ray, and the motion of the planes as well, between each frame. However, I'm a little stumped as how I would use this to find their future intersections over time, and whether that would ever possible time efficiency wise. I've read of some methods for reducing the need for complex computations such as octtrees and hit boxes.

I'm fairly new to this topic, so any resources, or advice on how these problems are usually handled would be appreciated. Thank you for your time!