Like anything else, engines work better when they're clean. But cleaning an engine is not the same as cleaning the rest of your car. Here's how to get your engine in tip-top shape.

[edit] Steps

Warm up the engine slightly. Do not get the engine to operating temperature, but allow it to run for a minute or so if it is heavily soiled.
Move the car to an area where the soap and material cleaned off will not cause damage or enter a storm drain. If you do not have access to a suitable location, take the vehicle to a car wash with an industrial wastewater treatment system. This is especially important if there is a lot of oil and sludge residue on the engine.
Remove the negative terminal cable on the battery then the positive.
Cover any exposed electrical components with a plastic bag or plastic wrap. This will prevent the electrical components of the car from being exposed to water which will be needed.
Cover the breather or air intake and carburetor on older engines with heavy aluminum foil or plastic. You may choose to tape or tie this in place, since water can cause serious problems if allowed into this area.
Brush any loose dirt or debris from the engine surfaces, either using a stiff bristle paint brush, or a plastic bristle cleaning brush.
Mix a solution of "grease cutting" dish detergent and water, using about 2 cups detergent to one gallon water.
Brush your solution on the engine, working it into the dirtiest areas, wetting them thoroughly.
Get a garden hose. Thoroughly rinse the engine.
Consult the vehicle's service manual and look up material that will be needed to clean the engine block and other metal parts. For heavy grease, you may have to use a solvent like mineral spirits, but engine de-greaser, available at automotive supply stores would be better. Be sure to follow the instructions on the container.
Remove plastic after rinsing engine and cleaning away residue of whatever chemical that you used to clean the metal components.
Let the engine dry. Most engines with high energy ignitions will run with the plug wires (and distributer) wet, but may misfire or run "rough" until these components dry out completely.
Remove all the materials you used to cover electrical and fuel system components.

[edit] Tips

Do not wash sludge, oil, or grease into a storm drain or sewer system.
Using hot water will clean much more effectively. For very dirty engines, take the vehicle to a mechanic's shop and have the engine steam cleaned.

[edit] Warnings

Determine the proper procedure for disconnecting the battery. There are sensitive computer components in modern cars that need to be protected. Without following procedure, one may trigger service codes or damage the onboard computer.