Well I'd recommend you to start out simple. Use the bounding box, understand the mechanism behind it and then apply it on other "simple" objects such as spheres, piramids, etc. Once you've done all...

In 2D it's more or less simple no?

Check if one of the corners (read: vertices) pokes into the area of another square.

You can calculate the location of each vertex when you know the center of...

Tell them if they are within range...

Do a simulation in your head of 2 cubes having 8 vertices and 6 faces each. See if you can come up with any rules for collision.

PS:
The external library...

I think this comes down to:

Does it cross this line/face.

For a 3D-object you'd have to at least have a bounding box. When an other objects is IN the bounding box (easy to check) check if it...