Digital reverbs generally come in two flavors.
Convolution Reverbs convolve an impulse response and a input signal. The impulse response is often a recording of a real room or other reverberation source. The character of the reverb is defined by the impulse response. As such, convolution reverbs usually provide limited means of adjusting the reverb character.
Algorithmic Reverbs mimic reverb with a network of delays, filters and feedback. Different schemes will combine these basic building blocks in different ways. Much of the art is in knowing how to tune the network. Algorithmic reverbs usually expose several parameters to the end user so the reverb character can be adjusted to suit.
The A Bit About Reverb post at EarLevel is a great introduction to the subject. It explains the differences between convolution and algorithmic reverbs and shows some details on how each might be implemented.
Physical Audio Signal Processing by Julius O. Smith has a chapter on reverb algorithms, including a section dedicated to the Freeverb algorithm. Skimming over that might help when searching for some source code examples.
Sean Costello's Valhalla blog is full of interesting reverb tidbits.
