What is the best way to clean up the engine compartment? Thanks

 

engine degreaser and low pressure water. You can also use a brush to clean stubborn dirty areas.

simple green is a good cleaning product, but just about any engine degreaser you find at auto parts stores will do a decent job on their own.

Don't forget to cover things like the alternator (if you can), air filter if you have an open filter, distributor, etc. You don't want water getting into places like those, thats also why you don't use high pressure water.

 

just too add to above:

make sure the engine is warm, not hot when you do it. spray the engine down lightly first, then use a straight simple green spray on everything. Let it sit a few mins the spray off. Take off the plastic bags from filter, alt, dist, fusebox and turn on car. Let run till mostly dry. Get any standing water with a towel.

You can use a towel and the simple green on any missed spots.

I always finish by wiping everything down with Meguiers vinyl and rubber dressing.