Hi Elizabeth, it depends on the size of the area. In some cases, if its just where people walk etc. Bringing in mulch or pea gravel can really help. If its a major mud problem, you will need to dig in a drain. Even several holes at least four feet deep filled with rock then covered with dirt would help a lot.
Straw or Hay. A quick and inexpensive temporary fix for a muddy yard is to put straw or hay down. If grass seed is planted first the straw covering can give it time to sprout and take root. The straw covering will allow your dogs to play outside without tracking in mud and dirt.
Is this a permanent fix or just temporary at a County, state or federal campground?