Remember to breathe... I've heard it helps... :)

Extremely hard to "get" early on, but try to only tense the muscles you are actually using for the work. Ground work is a lot of core, but often times new people feel stiff as a board. They can't understand why some people slip around them like a breeze. Being less tense helps facilitate your movement.

Early on, don't put so much into learning all the cool subs, focus primarily on defense and escapes. Try to want to win LESS and just focus on learning. Show up to class regularly, keep your mouth shut i.e, "I watched this Boobtube video on such and such" or "that wouldn't work doing such and such".

Most of all calm down, new people are notoriously nutty on the mats. Most injuries are accidental not intentional.

Good luck!