It's not a garnishment, it's a levy. HUGE difference. A garnishment requires a court order while a levy does not.
The IRS only resorts to levies if you have been ignoring them for an extended period of time. It starts with a gently worded request for payment which is followed up each month by increasingly threatening demands for payment. The final demand is sent by Certified Mail, Return Receipt Requested and warns you that if you do not either pay or make satisfactory payment arrangements that the IRS will commence enforced collection actions including bank and wage levies, property seizures, etc.
The IRS never notifies you by phone or e-mail. They ONLY notify you by First Class letter mail. If you moved and failed to notify the IRS of your new address and failed to put in a change of address notice with the Post Office, you screwed yourself.
The money is gone and they only way that you can get it back is to either prove that you didn't owe it in the first place or prove that the IRS failed to follow procedures in seizing the funds from your bank. They will provide proof that they notified you and that the notices were either returned as undeliverable or were not returned at all. That leaves you with proving that the debt didn't exist in the first place, however once the IRS resorts to levy action it's generally too late to appeal the amount alleged as due without going to the Tax Court.
If you still owe the IRS anything, contact them NOW and set up a payment plan. They can levy your account again if there is still an outstanding balance and you fail to make arrangements.
For future reference, any time that you move, send the IRS a Form 8822 http://www.irs.gov/pub/irs-pdf/f8822.pdf and put in a change of address at the Post Office that services your old address. Had you done so, you would not be in the mess that you are now.