You can do this as a part of an event. Check out the links to 24-hour events on my webpage here:
http://www.machka.net/links.htm
First, build up your mileage and do a century (100 miles). That's a milestone ride for most cyclists. See how you feel on that. Make note of things you would do differently for a more comfortable century. A few weeks later, ride another one and see how you feel on that. Then move up to a double century a few weeks or a month or so later. Your nutritional intake might change for that ride (you might need to eat more), and you might need lighting, so you can experiment with that.
While you are building up mileage on your training rides, do some rides at night to work with your lighting issues. Ride in all sorts of terrain, and in all sorts of weather conditions. Experiment with food. Experiment with your bicycle setup.
Incidentally, the ideal day to do a 24-hour ride would be about June 21st, but you might not be ready for that this year.
Here's my article with tips for riding a century:
http://www.machka.net/century.htm
And here's the UMCA website with tips on riding anything from a century on up:
http://www.ultracycling.com/