I cleaned mine outdoors at the end of the season , (that and painting a closet are two things that I never look forward to doing, nobody sees them, but they have to get done.)
You could check the end of my glog out from 2012 or to sum it up... I rinsed the trays with water, I had one 20 gal utility tub filled with diluted dish washing suds and a 20 gal diluted with 1/2 gal of bleach and water (wear gloves). The trays and pots would get scrubbed with a stiff nylon brush while in the suds, rinsed off once again with water then dunked in the "clorox" solution and scrubbed with another nylon brush. It doesn't have to spend any longer in the bleach then the time it takes to scrub. The trays were rinsed once again and finally dryed off outdoors in the sun.
You can use a slop sink/wash tub indoors and possibly getting away with a bottle bleach spray. This may seem like a waste or odd to some folks, but I haven't had any indoor pest
issues in years...outside of the occasional fungal gnats. The problem with the trays and containers is that either scale, mealy or white fly eggs can stick to ridges, creases and under lips on the trays outside of what my be lingering under some left over soil or debris in the bottom of either.
Sorry for the rant, but its one less worry and becomes a "clean" start for the plants during your indoor grow
Greg