Popular Mechanics has an interesting article up on the science behind the making of antivenom. The article discusses the "milking" of the snakes, the processing of the extracted venom, the inoculation of a host animal with trace amounts of venom, extraction and purification of the antibodies produced, and how the end product is used to treat snakebite victims.
One of the most surprising comments in the article related to the host animals used to produce the antivenom antibodies:
Considering that the whole process starts with handling angry, poisonous snakes, the comment about sharks not being easy to work with seems especially amusing.
The article also mentions a more personal method for antivenom production, as practiced by Bill Haast, the legendary snake wrangler:
Head over to Popular Mechanics for the full article, or take a look at a YouTube video showing how the snake milking is performed: