You rang?
No magic to it. I wasn't really the primary person out beating the bushes, and cold-call selling has never been something I enjoy or am good at, but that's essentially what it takes.
First, figure out and document exactly what someone's getting for their sponsorship dollars. For anything more than about $100, it should be something permanent. If it's connected to a course improvement, it should be displayed as close as possible to the improvement, if not actually a part of it.
Put together a potential sponsor package that includes a description of the project(s) that the funds are intended to help with, a rationale for why the project(s) are needed and are a priority right now, whatever information you have on the usage/popularity of the course (i.e., how many people can be expected to see the acknowledgment of their sponsorship and for how long), a description or even better a sample of how their sponsorship acknowledgment will appear, and a brief agreement describing the financial and other terms of the sponsorship -- how long the acknowledgment will remain in place, any special stipulations about location (hole number, not on the same hole as a competitor, etc.). Also cover details about who is responsible for production costs and provide information on requirements for materials like graphics, logos, etc. (sizing, file format, color constraints, etc.).
Present your proposal in a professional and businesslike manner, so that potential sponsors have all the information they need to make an informed business decision and so that they have confidence that they're turning over their hard-earned funds to people who have a certain level of competence and responsibility and are taking that responsibility seriously. Unfortunately, there's still a certain set of stereotypes associated with disc golf, so do everything you can to reassure them that their money won't be disappearing the next time 4:20 rolls around.
If you're doing tee signs or other types of signage, have a sample of the sign made if possible in the materials, etc., that will be used for their sign. Have a picture (even if it's a composite done in Photoshop) of what the sign will look like in place on the course. If you have the time and energy, go so far as to do a custom mockup or photoillustration of what their actual sign would look like in place (be careful on this with large, very brand-conscious organizations like national consumer-goods and restaurant companies -- they can be very jealous of unauthorized use of their brand names, trade marks, service marks, and "trade dress" -- i.e., the visual look-and-feel of their products and marketing materials -- but this should be an issue with smaller, local companies). If making samples isn't feasible, get samples of the general type and size of signage you plan to produce, where possible. The more tangible you can make it, the more likely they are to respond positively. Obviously, for printed materials like a scorecard, caddy book, course map, etc., it should be relatively easy to produce and distribute samples with your proposal.
As a final thought, if at all possible plan to produce some version of the acknowledgment item and give it to the sponsor along with a letter of thanks. We didn't do this, but in the future we'll be producing a duplicate of the tee signs (since they have to be produced two at a time anyway it doesn't significantly increase the costs) and mounting it in a manner suitable for display in their place of business; we probably won't do it in the case of individual donors/sponsors, since there is a cost involved, but having something for a business to put on the wall reminds them and their customers every day that they're supporters, and also serves as a cheap way of getting the word out to other potential business sponsors. If whatever you're doing is too large/expensive/whatever, then produce something inexpensive suitable for display.
Our local parks and rec department does not allow any sort of permanent advertising banners or signs to be mounted to any permanent park feature or structure. They do allow sponsorships of particular groups or leagues for the duration of a season, however, so sponsors typically produce large silk-screened banners that can be readily taken down, stored, and reused. However, for our tee signs, they regarded those as being an acknowledgment that the construction of the concrete tee pads and tee signs was made possible by the contributions of the sponsoring companies, and so allowed them. Policies will differ in different jurisdictions, so just make sure you understand clearly what the constraints in your situation are, and that the relevant authorities know and approve of your plans.
Once you have the sponsorship proposal package ready, it's time to go sell. But to whom? Obviously, part of the answer is to start with people/businesses that have some connection to the disc golf community. Have everyone involved hit up their employers, spouses employers, etc. if feasible. Any retail stores that sell discs and/or accessories are also obvious targets. Next on the list should be businesses in the vicinity of the course that could reasonably be expected to draw customers from among those playing the course -- bars and restaurants (again, make sure there aren't any issues with local policy on advertising alcohol, tobacco products, etc., and that you understand those constraints before you pitch those businesses), convenience stores, grocery stores, drug stores, etc.
If there's any upcoming event or occasion that you can use to promote a sense of urgency, do it. In our case, I doubt we'd have sold 9 sponsorships in our initial push (just enough to do one set of tee pads of our three sets) if we had not had a National Tour event coming up roughly six months after we started the effort -- indeed, the reaction of tour players to the crushed stone pads at the previous year's event made it clear we needed to address that if we wanted the area's first NT event in many years to be a success).
Do everything exactly right and you'll only fail most of the time. We've approached every business we can think of nearby, and some farther away. Of the 18 holes on the course, we have sponsors for 11 now. We sold 9 in our original push between fall 2008 and spring 2009, and have only sold 2 more since then. Of those, 5 were purchased by individuals or families (non-businesses), 4 by businesses that had some personal connection to the disc golf community (in each case, disc golfers as the business owner or senior management, including one disc golf-related business), and only two that had no personal connection -- a Mexican restaurant across the street from the course, and our local PGA Tour Superstore, which recently started selling disc golf gear and has been very financially supportive of disc golf so far. It just takes asking a huge number of businesses to get a very small number of "yes" answers, and unfortunately none of us has the time to devote to it in order to get to those yeses.