Don't talk about how you did things at your old job. It's a big temptation, but a serious mistake.
Don't bluff. If you don't know how to do something, ask.
Acknowledge your mistakes. You're bound to make some; don't try to cover up.
Ask questions, take notes. Most people don't mind explaining things to you, but they'll lose patience if you ask the same questions over and over.
In office jobs, don't dress too casually. One common suggestion is to dress for the job you want to have, not the one you already have.
Keep your boss informed. No surprises or embarrassments.
Study the employee handbook. Pay close attention at orientation and training sessions.