At the most basic level, make sure that you practice the events like they will be at competition. This means, full safety gear, arm restraints, full cones (inside and OUTSIDE of skidpad). Even good drivers sometimes choke, so it’s good to get them very used to the events so there is less pressure the day of the events.
Practice tight autocross courses with minimum radii turns and slaloms. I hate this, it sucks, is not fun, etc. but SAE courses will have these aspects to them, and you can really loose a lot of time if you find that your car can't steer enough or that the steering is too heavy.
Unless you don't have a choice, I would not start new drivers out in the fsae car with slicks. Slicks are tough to drive on (and expensive!) and also, slicks plus lots of power can be disastrous because there is very little room for error before the tires slide out. Coupled with parking lots, curbs, poles, it can be dangerous. I agree with the other poster that go karts are a good starting spot and even I learn a lot from them (running endurances and such).
Good luck, be safe.