To get a paying gig in a club, the person you need to talk to is the club's booker. The booker will decide whether to book your band based on your demo CD. So it's a good idea to have one.
Your demo CD will have anywhere from three to 10 songs on it. The first song should be your best -- you've got to keep the booker listening. The CD needs to be professional-grade, sound great and cause the booker to sit up and notice. The CD label should have your band name on it and -- pay attention -- your contact information. Put someone's name and phone number on the CD label so that if the booker loses everything except the CD, he can still reach you. For information on how to produce this great demo CD, check out How Producing a Demo Works.
The "everything else" the booker might lose is the package you create around the CD -- the aura of your band, if you will. The demo CD is the core, and you've got to remember that you're not just conveying information; you're conveying an image. So put some thought into it. In the package you want a good 8x10 photo of the band, a one-page bio of the band and a one-page summary of any press clippings, if you have them. If you've played anywhere "big" -- a place that is impressive or at least recognizable -- be sure to list it.
The last thing you need in your package is a one-page cover letter. You'll have to customize the cover letter for each club you send your package to, but if you put some effort into a standard form you'll have a good base to work with so you'll just have to change a few words each time you submit it. Basically, your letter needs to explain why you are the right band for this club and how many people your band can potentially draw to the club when you perform. If your band has an e-mail mailing list with 2,000 local people in it, you should say that. If you recently played somewhere and drew 200 people, you should say that. The cover letter should let the booker know that your band is "real" and why that particular club should care.
Once you have all of this material ready to mail out, you can call a booker.