What is the science behind making actors appear different?

I know for LOTR, the long scenes in the house of Bilbo, they actually made two versions of it. One small one, and one big one. In the small one Gandalf would be too big, and in the other one Bilbo would be extremely small.

Using digital effects, and other techniques mentioned in the comments, these two can be merged together to get the effect they were after.

I also noticed in the extended edition of the Return of the King, that in the final scene were Frodo leaves, you clearly see body doubles walking towards the boat (proportions are different, they are clearly kids instead of adults).

In The Social Network, Armie Hammer plays both of the Winklevoss twins utilising a method that allowed the on screen presence to be recorded with a body double (Josh Pence) with Armie's face subsequently digitally replaced over the top for scenes with both twins present.

Here is a video detailing the process a little bit.

Director David Fincher further explains;

Hammer played the main twin in each shot. For shots that included both twins at the same time, Pence stood in for the second twin; Hammer later went into a studio, where he strapped his head into a harness to film that twin’s face and voice, which was then digitally superimposed over Pence’s face in the film. The result is a sort of hybrid actor with Hammer’s head and Pence’s body. Intricate split-screens and rotoscoping were also used for some shots. Piece of cake, right? “After Benjamin Button, you go, ‘It can be done,’” says Fincher. “Give us a case of Red Bull and a weekend, and we’ll figure this out.”