Know the fee allocation and other relevant financial procedures of your college. Refer to your development office for specific information about your institution.
Get to know the academic division heads and administration officials. Attend staff functions in order to establish working relations with those who have power over fee allocations, donations, and development.
Keep your own debate/speech alumni informed of the activities of the team and department. This information to alumni really helps when it comes to fund raising because alumni are much more likely to give when they know where their money is going.
Be sure to submit major team accomplishments throughout the year to any college publications that go out to alumni, parents, staff, faculty, etc. Also, try to get beginning-of-the-year and year-end summaries to such publications to pique interest about the team within the college community.
Keep careful records of your own team's budget in order to have adequate documentation to submit to budgetary committees. Such documentation makes fund disbursement easier for the committee and makes your chances of getting adequate funding greater.
Do your own research on how to apply for endowments (See the Cost Committee Endowment Sheet). It's easier to get involved in college budgetary processes when you know the details of those processes.
Keep your team visible and accessible to the college community. Host open houses for incoming students, consider an intramural debate tournament, keep other faculty, staff, and administration abreast of the team's performance. Make sure your students pre-arrange absences with their professors. These may seem like piddly details, but in the college environment, little things mean a lot and attention to such details will get more influential individuals within the college community on your side.