You need to fill in the forms.
Online will telol you exactly which forms you need and I think (although may have been inland revenue site) you can order the forms online.
Transfered a plate last year adn it took about three weeks.
You'll get the certificate of ownership back which is valid for a set time so's that you can get a plate made up - then sometime after that you'll get the new log book.
don't even bother phoning dvla - waste of time and money.