Recently I shot the mud factor 5k run in San Bernardino, California. I got stationed at the finish line waterslide which ends in a giant mud/water pit. I got covered head to toe in mud and water, as did my camera and gear. I shot a Canon 6D with a Canon 24-105mm L lens.
To start cleaning, I start with a distilled water and isopropyl alcohol mix. About 75% water and 25% alcohol. A large microfiber cloth is recommended to clean your camera. It is also preferable to use a UV filter to protect your lens from dirt and scratches. Please don't forget to turn your camera off and remove your battery before cleaning. With the microfiber cloth damp, not soaked or dripping, gently wipes away any dirt and debris on your camera and lens. It is best to rinse your microfiber cloth between wipes.
Once your camera has been cleaned of most dirt and debris, you can start using cotton swabs dipped and squeezed in your water solution to clean in-between small and tight areas.
Using a manual air bulb, gently blow any dust and dirt that may still be on your camera. Your camera should be fairly clean at this point. The next step would be to remove your lens. Be careful of any dust or dirt that may be trapped between your lens and camera body. If any dirt is visible, use your air bulb and cotton swabs to clean the area before you remove your lens.
Once your lens is removed, carefully inspect your camera body to lens connection for any dirt or debris. With a new microfiber cloth, gently clean the contacts on your lens and camera body, dry with no solution.
You may either re attache your lens to your camera or place a body and lens cap on your gear to protect it from dirt and dust.
At this point your camera should be good to go. Further inspect buttons, eyepiece and other small areas for left over dirt.
To get rid of excess moisture from your camera and lens, there are a few ways this can be achieved. You can buy a commercial dehumidifier or make your own with a airtight container and silica gel. Silica gel can also be purchased in packets that can be left in your camera bag to help reduce moisture.