One of the most important things to do is to bring a tripod wherever you go. Without a tripod, your shots automatically go form awesome, to not so awesome. Shaky shots are horrible, especially when you are in a competition, because steady camera work can be the difference between winning. Bringing a tripod also makes it easier to film because you don't have to hold the camera the whole time. Basically, having a tripod just makes your filming life easier.
Before you go to shoot something, you should always make sure that you have previously adjusted your camera settings. This usually includes the white balance and the recording levels for the audio. You want to do this so that you don't waste valuable filming time. If you are shooting an interview, you can also waste the interviewees time. While you may not know exactly how loud your actors or interviewee, or how bright a day it will be, it is always possible to just take an educated guess.
The third thing you should always do is to bring backup equipment. As Murphy's law states, "Everything that can go wrong, will go wrong." This really happens, so the best thing to do is to come with backups. Always bring spare batteries and SD Cards, and try to bring a backup camera.
All in all, I have gained a couple of pointers through three years of working in this class. These tips are to always use a tripod, always adjust camera settings before you go shoot, and never leave without backup equipment.