I want to tackle some basic 3-D collision detection and was wondering how engines handle this and give you a pretty interface and make it so easy ... I want to do it all myself, however.

2-D collision detection is extremely simple and can be done multiple ways that even beginner programmers could think up:

1.When the pixels touch;

2.when a rectangle range is exceeded;

3.when a pixel object is detected near another one in a pixel-based rendering engine.

But 3-D is different with one dimension, but complex in many more so ... what are the general, basic understanding/examples on how 3-D collision detection can be implemented?

Think two shaded, OpenGL cubes that are moved next to each other with a simple OpenGL rendering context and keyboard events.