Are you talking a restoration cleaning or an annual cleaning?
For daily use, I just use a good quality grill brush. Its best after the cook, when the grill is still hot,
Lightly oil your grates to keep them from rusting. Sweep out the cold ashes with a whisk broom.
Hose it out once in a while when the mood strikes me.
For a restoration clean up, it gets more involved..
First assess the grease and grime. If its heavy, I use Heavy Duty Easy Off.
I always disassemble first. Easy Off is harsh and dangerous, so caution is Key. Some recommend spraying it on, then stick it in a plastic trash bag and let it soak in the sun.
Dawm Dish soap and SOS pads or 0000 Steel wool for the inside and outside of the bowl.
The charcoal grate gets a stiff wire brush to knock off the loose material.
For the charcoal grate, (Assuming its salvageable, I break out my Grinder with a 4" wire wheel.
Again, this is dangerous and caution is key. Some grates are too far gone and I just replace.
Sometimes a plastic scraper is all you need. I have had to use a razor blade to scrape off the carbon encrusted burnt on gunk. It takes time!
Hope that helps!
AJ