We have a baby and a toddler so there's a LOT of washing going on here. I streamlined the whole process, it was a lot of work but I'm so glad I did.
First I moved the washing machine into the hall cupboard next to the bathroom (this freed up space to put a dishwasher in the kitchen and also meant the machine is situated where most of the laundry is created). Then I put 4 big white IKEA crates on a shelf above, labelled "darks", "whites", "colours", "delicates" and a vertical basket to the side for cleaning clothes, tea towels etc. The dirty clothes go straight into the correct crate and every time one crate is full, I throw it all in to wash. On my weekday off, I also do the bed sheets and towels.
I don't tumble dry - I dry outside in the summer but for the rest of the year I installed a double decker pulley airer which hoists 2-3 loads of laundry up to the ceiling above the loft bedroom stairs.
I use multiple socktopuses - one for us, one for the kids, and make sure I sort laundry as I'm hanging out to dry.
I use the timer on the washing machine a lot - throw a load in whenever I get a moment and if there's not room on the airer straight away, set the machine to wash first thing the next morning/just before I get in from work.
Finally I Marie Kondod the drawers - bought dividers from IKEA and started folding everything so it sits vertically and can all be seen from above. This way I can open a drawer and see all the t-shirts at once, meaning I don't have to rifle through it, messing everything up. It's really quick to put things away as there's a box for short sleeved tees, a box for long etc.