First of all, congratulations! That sounds like an exciting opportunity. Much like other high school, collegiate, and public recreational facility tracks, an Olympic sized track measures 400 meters around, when in lane one (i.e. the lane closest to the inside field). One mile is 1600 meters, which equals four laps around the track in lane one. If you know how far you will be running for the race, you can go ahead and calculate how many laps around the track you will be running.
Depending on the race, you might have to stay within your own lane. Shorter race distances on an Olympic track stagger the runners' starting positions so that they all run exactly the same amount (even if they are positioned in one of the outermost lanes). Longer distance races still stagger starting positions, but runners are allowed to leave their lane and join the "pack" that forms in lane 1, since that is the shortest distance.
As far as training for the race is concerned, it is all about whatever distance you will be running for the race. If it is a shorter race (anywhere from 200 meters to 800 meters is considered a "shorter" length) then you will want to focus on incorporating some speed drills into your training runs. If the race measures longer in distance (anywhere from 800 to 3200 meters, or even an entire 5k) then you will not only need to make sure you have built up your distance running endurance, but also you will want to prepare yourself mentally. Running distance races on a track can be mentally taxing because scenery and elevations do not change. Instead of running through beautiful, winding trails or along race routes that run by buildings, homes, people, and rural landscapes, you are running around the same circle over and over again. (The plus side, though, is that running on a track often means running surrounded by bleachers and cheering spectators who can be all the encouragement you need to perform well!)