Keep a record of your efforts to obtain new employment.
You should start keeping a record of all of the efforts you make to locate replacement employment. Beyond the mere on-line application record you may be required to post to obtain unemployment benefits, you will want to keep written records of dates/times/locations/job titles, etc., of all positions you apply for, people you speak with, interviews you attend, etc. Depending upon if there is a requirement in your underlying order you may need to provide a copy of this record to the Court (or the Florida Department of Revenue if your order entered in a Title IV-D case) each month, and be prepared to bring such records to any hearings set upon Motions for Contempt against you, to demonstrate diligent job search efforts and why any nonpayment was not willful on your behalf. You may also need to register with job search companies, state agencies, etc. - check the language in your order.
File a Supplemental Petition to Modify Child Support.
You will need to file a Supplemental Petition (not a mere motion) to Modify the Child Support, alleging that an unanticipated, involuntary change in circumstance has occurred (e.g. you did not voluntarily reduce your income) and detailing the facts supporting why the change is substantial and warrants modifying the support obligation. You will need to file a current Financial Affidavit, and have the other party served with the Supplemental petition, the financial affidavit, a summons (and depending upon your local rules you may also need to provide copies of the old Financial Affidavits and guideline worksheet that the Court based the prior support upon). It is important to note that the Court will only be able to modify the obligation retroactive to the date the Petition is filed with the Court, so if you wait six (6) months after you lose your job to file for the modification, the Court will not be able to go back in time to help you any early than your filing date.
Make a good faith effort to comply with the prior order.
You will want to make sure to make whatever partial payments you can throughout these proceedings, to demonstrate your good-faith and clean hands in seeking the modification - not to mention that the children no doubt rely on your support contributions and these partial payments will go a long way to demonstrating to the Court that you recognize the child(ren) have an ongoing need - even during your time of reduced income/earnings - and that you're trying to do the best you can.