Before you start work on your engine, you might find that warming your engine, and letting it run for a minute or two, helps to loosen off some of the dirt. Warmth can make the grease, mud and whatever else slightly more malleable, meaning that it can be scrubbed off.
Since you will be working with water, it is important to cover all of the electrical parts of your engine in order to prevent water from getting in and damaging your circuits. The distributor, air filter, coil, and the oil dipstick will all have to be covered over. Use plastic bags from supermarkets and elastic bands.
Use a degreaser to really get to the dirt. This should be non-alcohol or petrol based. A citrus domestic cleaner will do the job well. Leave for a couple of minutes, and then sub over with water, using a toothbrush to remove any obstinate dirt.