I don't have a washing machine, nor can I afford one as of now so I wash my clothes by hand...
It sounds weird but actually using the bath isn't so bad, it takes me about half an hour to wash about five or six machine loads because the bath's fairly big compared to a washing machine.
Step 1: Hot Water, Washing Powder.
You'll need to get yourself some washing powder for hand washing, whether or not it's different by a huge amount I don't know, if you have your own preference to wash with most brands have a version, usually hand wash and twin tub is the name.
As for water you'll only need to the immersion/heating on about a third of the time to get enough to fill for washing.
I only filled the bath a bit in my photos because I didn't have to wash as many clothes as usual, I rough guessed the amount to be around 40L, so I poured in what felt right, it'll vary powder to powder but a rough estimate should be OK, if you go really overboard you'll need to rinse your clothes a few times before drying.
The temperature doesn't need to be anywhere near a normal bath, unless you like them lukewarm,
Step 2: Rinse
You do need to rinse your clothes out, depending on what makes more sense you can dump them all out and refill the bath with water, it doesn't need to be warm, cold will do or rinse them out under the tap as you go, depending on how much room you have left in your bath.
Also you'll need to give your bath a good rinse out, I don't have to many clothes that make lots of lint so the normal plug is fine but you may find throwing a bit of mesh over the plug hole is a good idea.
Step 3: Squeeze and Hang Out to Dry.
You'll want to squeeze your clothes out as best as possible before hanging them up, to get as much water out as possible.
I carry mine down in a big blue IKEA bag, whatever you use give the bottom clothes a second squeeze before hanging out as they'll likely be soaked again by the clothes on top.
hang them up and dry them out, during winter I have intentions of hanging them up in the old laundry room and putting a little fan heater in to turn on intermittently to dry them out, since there's a dryer outlet in the room I'll probably get away with using another fan to make the room in to a big dryer.