Compete, do well, and keep records. Your race resume should reflect your place in the race as well as the field size (finishing 10th in a field of 200 is obviously a better result than finishing 10th in a field of 11!) Then, register with a web site like loop'd, or contact local sponsors - bike shops, businesses you know/use. Most sponsors have an application window - usually closes in Oct/Nov. Most applications will include a request for a race resume and personal bio. It never hurts to include a personalized mention of how you use the sponsor's product. Make sure you spell check your submission.
Pick up a few biking magazines and carefully read all the ads. Visit each advertiser's website, and look around for sponsorship information. Read their criteria, and if you feel you qualify, follow thier directions for sponsorship application. Do not request sponsorship from a company whose products you do not or would not use - for example, if Specialized sponsors you, don't be riding a Trek.
Once you get sponsored, remember that you now represent your sponsor - you are a rolling advertisement. When you are on your bike, you are that company, so act accordingly. You and your language should be polite and respectful to those around you. You should always seek out the race organizer to thank him/her for organizing the event. If you podium, have a clean jersey handy. Remember not to cover up your sponsor's name on your bike/kit. Keep in touch with your sponsors - provide race results/pictures on a regular basis.
As with mud, life, too, slides by.