(1) File your bankruptcy petition and get your bankruptcy case number from the court.
(2) Call the attorney that sued you on behalf of your creditor. Tell them that you have filed bankruptcy and your case number. Let them know that the automatic stay protects you from any further garnishment of your wages. Make sure you have the case number from the state court case when you call them so they can look up your file easily. You can find the case number in part 4 of your Statement of Financial Affairs (Form 107).
(3) Call the creditor that sued you and is garnishing your wages. You can skip this step if you'd like. The most important part of this process so far is Step (2). Once the attorney knows, the burden to make the garnishment stop is on them.
(4) If your wage garnishment involved the sheriff's office, make sure you notify them about your filing and provide them with your bankruptcy case number.
(5) Let your employer or payroll company know. They likely won't be able to do anything until they get a formal notification from the state court, but this at least puts them on notice.
(6) Follow up with your employer/payroll department frequently. Don't wait until the next payday to check the status. If necessary, call the creditor's attorney again to follow up.
While this may sound like a scary process, you're mostly acting as the middle man, making sure that everyone is on the same page and is doing what they need to, so your next paycheck is not garnished again. Ultimately, if the creditor fails to take the necessary steps to stop the garnishment, you can ask the court to sanction them. The creditors - and their attorneys - know this and generally don't want to get called into court to explain their actions.