I've done this successfully for continuing education classes at both community colleges and public universities, both for pay and for free (for marketing/exposure). You didn't specifically mention continuing education but I think that's much more realistic if you want to teach a class that is not currently offered.
To pitch a class to a continuing education department, I'd recommend your prosposal contain a course outline as well as why the class would be a nice addition to their offerings and why you're the one to teach it. My understanding is that many continuing education departments are hungry for exciting new classes where 1) they don't have to pay the instructor much and 2) the instructor is not going to use the class as a hard sales pitch.
If you want to teach a for-credit class that already exists, kick into "job hunt" mode the 48-Days way. For this you'll likely need at least 18 graduate hours in the field you want to teach in, unless the class is "Development Math", "Developmental Reading", "Developmental Writing" ESL, etc., for which a relevant Bachelor's degree might be enough.
If you want to teach a for-credit class that doesn't currently exist, you should probably talk to the department chair to see what the options are for this. Again, I'm guessing you'll need at least 18 graduate hours in the field you want to teach in, if not a Master's Degree.
The lead time for much of this can be several months -- now would be a great time to talk to colleges about the fall semester, particularly for new course offerings.
I'll just add that being a part-time instructor of for-credit community college classes can be a nice way to supplement income while a student or while transitioning from a full-time job into self employment. If making money now is the goal, for-credit classes pay much better than continuing education ones.
If the above doesn't really answer your specific questions, provide more detail and I'll see if I can add more to this.
Reid - Thanks for all the great information. I'm had similar thoughts about pursuing a position with a continuing education class. I was just debating whether to also pursue sometime on the university level. I think after reading your comments I'll will continue to pursue the community education route and then build from there. Your suggestions for what to include in the application were exactly what I was looking for.
I also like your comment of doing a free class for marketing purposes. That is a great idea. How successful has that marketing tool been for you in the past? Like you said, you want to provide great content without making the class just another sales pitch.
I will be working on this over the next couple of weeks. I'm very excited to move this forward.
I used to do classes at a community college and for a computer training company. I don't remember what sort of proposal I put together, but I do remember they don't pay particularly well. The one area that I made money was doing continuing education classes for teachers because I got paid by participants and they tended to be well attended.
Depending on what you are planning on teaching you may want find ways of offering continuing education classes for specific groups. I know several people who have developed programs for CEUs that they charge a premium from.