Cut your grass with a lawnmower. Mowing the lawn helps remove the dirt that is resting on the top of the grass and will help get the grass more sun exposure by taking away the top layer of dirt from the grass blades.
Rinse the grass with a sprinkler. Use caution because excess water is what likely caused the dirt buildup to begin with. Rinse the grass off without flooding it or else you could make the problem worse.
Pull out any muddy grass that is starting to die. Dead grass can contribute to other muddy grass forming since it doesn't irrigate as well and can contribute to water buildup that causes mud. Pulling the grass out removes the dirty eyesore while also improving irrigation.