A race can be anything you want - point to point, around the buoys (either fixed or set marks) or a combination of the two.
A conventional Hobie Cat race is around set marks, but that can take a lot of equipment. For example, at Midwinters East, we had as many as 9 marks in the water at any given time, with three mark-set boats and a race committee signal boat.
Even a "minimalist" set mark course requires two marks and two motorboats. (You can do it with one, but it can cause delays as you run around to adjust marks that might be a mile apart.)
Typically one mark (weather mark) is set some distance upwind from the signal boat, where the starting line is set. The distance is determined by the type of boat and wind speed such that it takes the first boat racing about 12-15 minutes to get to the weather mark.
You can set a separate leeward mark or gate, or you can just use the starting line mark as the leeward mark.
The race is either two or three laps, elapsed time for the first boat should be 45-50 minutes.
For your situation, a distance race might be more appropriate. Just determine where you want to go, put it in writing so everyone knows the course and do a LeMans-style start off the beach. No equipment required.
Regardless, here is the place to start - ISAF Racing Rules of Sailing
. Pay special attention to Section 3 (Conduct of a Race) and Section 7 (Race Organization)