I'm a white belt so maybe not the best advice but I feel like typing.
I think first off train with the best instructors in your area... makes a huge difference.
It's been said before but position over submission is very important, I find if I can control somebody I'll wear them out to make the submission a lot easier.
Start with the basics, I love the Gracie's because they focus a lot on them and they are what works.
Staying calm under pressure is huge, best example is watching BJ Penn. You could never tell if he was winning or losing a fight based on his demeanor... he is calm through and through and it helps him conserve energy.
I'm a little torn on the "tap early and often" point of view. If you tap too early you actually hinder your opponents ability to gauge an accurate assessment of that submission AND you don't really develop a taste for the shit-has-hit-the-fan-so-now-wtf-do-I-do ability that comes in handy. Personally I hold off on a submission until I'm totally pinned and have no energy left to escape or I feel pain starting (unless the guy is an ape and cranks submissions in practice, I'll tap early and avoid his ass). Only exception is leg locks, they don't usually hurt until something pops so those I don't play as much with those.
Hygiene is huge. Wash you clothes, air out your equipment and shower ASAP. Keep your nails trimmed back too, I have a scar on my thumb from a long nail.
Also train in judo and workout at the gym, you'll get better in takedowns (and takedown defense) and improving your cardio and strength will help you gain confidence in tougher situations.
Last, HAVE FUN! Sometimes I don't like going to the gym because I think I'm gonna be owned again and choked worst then a crack-dealer who swallowed his junk in-front of the cops... only to end up having a blast and learning some cool shit. Ask your instructor if somethings not clear, chances are if you didn't get it so didn't a few other guys.
Damn, I had a lot to say I guess.