Actually, crimson, I prefer to do my own washing-up too because I know I'm more thorough than most people. I'm very fussy about food hygiene and bathroom hygiene, but the rest of the house can go hang, and does!
My method? Well, very hot water for a start. I wear rubber gloves. Good quality squeezy. An assortment of cloths (microfibre favoured), brushes, scrubbers, etc., which vary according to the surface being cleaned. one of my faves and the most effective on Le Creuset enamel is a bundle of broom roots tied together (made in Sweden). Another is made out of maize husks. Non-scratchy but very effective both of them.
I rinse everything (collect a few things together in the tiny fairly useless sink that's next to the main one and do them together – quick swill under the tap).
Leave most things to drain naturally, although I often put a teatowel over the Rayburn and put the dish drainer on that after the dinner washing-up. Things dry quickly that way. I have a slatted metal shelf above the Rayburn too on which I put all those useful plastic boxes that are hell to get dry. Also bottles/carafes up there on a stick-bottle drainer.