C.C.
Well, the first thing to do is to change all of your automatic withdrawals to the new bank account. Then, submit a direct deposit form to your employer with the new bank account information. While you are waiting for the direct deposit to change over (sometimes 1-2 paychecks), you'll just have to withdraw the money from your old bank, and deposit to the new bank (or write a check from the old to the new, whatever's easier). It's a pain in the neck, but it will be overwith in a few weeks. :) Then, leave the old account open for a month or so, in case there are any outstanding charges. After the month is over, go in and close out the old account.
We had to do this a year ago, after being dissatisfied with our credit union. It wasn't actually as bad as I had anticipated!