Many areas have nothing but the standard exemptions for paying, which are based on type of debt, not your situation, so no form exists. Some have a form (like Calif, which changes from county to county...and starts in big letters all over it with - read the instructions), in others you would present your case in a letter.
Be aware...in any case you better do YOUR work and check to see if you have an actual basis for your claim....generally claiming it is a financial hardship really ain't going to fly - so find a reason that is qualified for exemption in the law of that area - (your not paying your debts is a financial hardship to those you owe...and the reason for the garnishment is you have failed to do what you were obligated to do (and in the eyes of the creditor/court, chose to pay others before them). Now, if those others are medical and real pure non-frills life support type items, you may get a sympathetic break...or if your wage/earnings are so low that any garnishment puts you into the poverty bracket for your area...(and even then, if the garnishment is for child support - you will rightfully have a tough time getting exemption).
In the few places that have a formal process to claim exemption I researched...you will have to provide exacting documentation to support your claim, including financial records, other court and medical records, etc. If your doing it in your own format, this would seem to make sense.