Coming to Dinkelsbuehl you will notice parking areas at the main entrances into the old town. In the case that you want to spend the day here it is recommendable to park on one of these parkings as parking in the old town is restricted by time. Here the parking needs a parking disc and the car has to be moved after 1 hours in the periode between 8.00 and 20.00. On the parkings outside of town, it is free and unlimited.
Check the link below for a map with the official parking areas.
You can get an allowance to park the car for long term in the old town from the city hall (4 Euros). But I think it is no problem to park outside as distances are not too long here.
It is by far, easiest and best, to park outside the town walls. There are 4 public parking places meant for such. It is metered parking. We paid 1 euro for a three hour visit.