I've done this and not particularly well. Here's some tips from experience:
1) Don't go dark. HLGEMs answer of checking in every day is a great one. Also bill promptly or on a pre-established schedule. In many cases the trust you've established as an employee erodes quickly as a contractor, you want to be as transparent and visible as possible. Also consider any travel or deadline obligations you might have with the new position and how that might affect your ability to do two jobs. Set expectations accordingly and live up to that standard.
2) As far as staying synched up with the rest of the team, make sure you send regular emails/IMs/wiki updates just saying what you're working on and reminding people you're out there. In a less formal way, try to get a couple former coworkers to keep you in the loop. Depending on how much of a problem this is, you might commit to taking a late lunch once a week and calling someone just to "water cooler chat" and keep the communication channel open.
3) Decide how long you want to do this. If you want to work two jobs, I would suggest setting up a retainer and/or an agreed support level (Up to x hours a week/month). Unlimited support on two jobs will burn you out and there will always be priority conflicts. If you're just helping out, you should provide incentive for your former employer to replace you quickly so you can move on. In that case I would charge at least 3x your previous salary as your hourly rate. That's fairly standard as they're no longer providing you any benefits other than a paycheck. If you want to stick with it for awhile you might pick a smaller number.
4) Assuming this is in US, familiarize yourself with 1099s and how this will affect your tax situation. There are a lot of wrinkles that aren't obvious if you've been a "normal" employee all your life.