On my offset, I use a wire brush on the grates when I take the meat off and then I usually let it sit overnight because I am pooped after fighting, er, feeding the thing for 10 - 12 hours on a big cook. Next day, I take a putty knife and scrape off the accumulated grease/gunk off the area below the cooking grates. It's usually still soft and comes off easily. Then I wipe it down with a paper towel and push any remaining liquid down to the drain. Use a wire brush reamer to clean out the drain and run a paper towel through it to finish up. I used to hose it out, but it tended to develop a little rust afterwards so I only do that a couple of times a year now.
BBQ Apprentice - Old Country Brazos offset, 22.5 WSM, Various gassers, portable grills, etc.