I think you sign up as normal, either by invite or just signing up without an invite, and fill out everything again. Most features should be the same as when you left (here is a quote from Leto's petpage about resubscribing)
Quote:
Note that after you resubscribe to Neopets Premium, your Premium settings will be the same. Your portal preferences should be restored, any referrals you sent out will remain the same, as well as any referral prizes that you have earned. If you were a Charter member, your chat board status will be restored as well.
Here is a great page with all the info you'll need about resubscribing
(Also, if you want an invite, *cough**cough* I have a few I could spare *cough**cough*)