What is the best way to clean the engine area at home. I'd like to avoid damaging the electrical system or other components present.
If it's a relatively older car and you want to take care not to get water where you don't want it, just get yourself a roll of those blue automotive grade paper towels and a bottle of simple green ( or a similarly gentle cleaner ) and take an afternoon to wipe down your engine bay. That way it will be easy to avoid damaging any wires. Sure, it doesn't sound as fast as just hosing things down, but your engine will thank you for it.
Steam cleaning is effective for older cars, but does require manual wiping down afterwards, and car taken around the fuse box or other electrical items in the engine bay.
Take extra care with the distributor as high pressure steam could get inside it and condense.