The simplest version, red/blue hackenbush, is played on a graph with red and blue edges like the one in the illustration below. The heavy black line at the bottom is the ground, and every edge in the diagram must be connected, directly or indirectly, with the ground. Players take turn "hacking" edges, where the red player can only hack red edges and the blue player, blue ones. When an edge is hacked, it is deleted from the graph together with any other edges that are no longer connected to the ground. The first player who is unable to hack an edge loses.
I have written a program called "hackenbush" that allows you to play red/blue hackenbush against the computer. There are a number of built-in games, but the program also allows you to create, edit and save games yourself. You can also put it in a passive mode where it can be used as a game board so two humans can play against each other. Documentation is included under the 'Help' menu. And complete documentation of the program with examples is available here: hackdoc.pdf
Hackenbush runs on Intel-based Macs or Windows machines. The program has been extensively tested on a Mac. On windows machines, not so much.
Here is a paper I wrote about the mathematical theory of Hackenbush aimed at bright high-school kids:
Here are the downloads for the executables for both Intel-based Macintoshes or Windows (tested on Windows XP and Windows 7):
Macintosh executable (in tar format: after you download it, double click on the 'hackenbush.tar' file to obtain the hackenbush.app file) Windows executable
The illustration below shows what the program looks like, at least as of the last time I did a screen grab: