1. Be cool. Nearly every mistake I've made was due to rushing things or freaking out (even if just a little).
2. Be prepared. Nearly every other mistake I've made was because I lit the fire before I took that little bit of extra time to get things ready. Preparation includes education, sanitation, knowing what your equipment is (and, to some extent, how to use it), and some degree of mis en place (i.e., putting things in their place - getting your ingredients and gear ready to go).
3. Be sober (at least for the first few batches or until you feel very comfortable). The rest of the mistakes I've made were because I got too far into my beer before I got far enough into my brewing.
4. Be realistic. You will make at least one mistake. Very likely, you will make many. Drive on.
5. Be a secretary. Take good notes on what you did (or did not do), so you learn from the mistakes you make.
6. Have fun!
TL