I grew up when my grandmother was still hand washing and using a wringer, they had gas fireplaces so they put the damp clothes on a clothes horse by a fire or in a warm room.

Bathtub works, fill with hot / warm water as needed and buy a detergent meant to dissolve for easy hand washing. Borax was often used to boost cleaning. You can pretreat stained areas with various cleaners, but borax pasted onto the wet area and rubbing the fabric face together on itself with two hands works. Its how you’d do collars and armpits too. Basically swish them around like the agitator did in the old style washers. Rub areas together with other fabric that you know need extra cleaning. Its about getting water to pass through and physical abrasion, and soaking to let soap attach and breakdown oils etc.

Rinse everything well after the wash part. Modern soaps for HE machines take forever to rinse, the non HE soaps may work better, ifbyou can’t find a good washing powder or liquid.

Then wring each normal item it by holding two ends and twisting it, and twisting it, it will self squeeze the water out as it tightens up like a rope. Don’t do this with delicate fabrics.

I have seen old roller wringers at the thrift store, you feed the clothes in and wind the handle and it squeezes the water out as it flattens you laundry.

Then hang to dry. Dry air helps, but if you have a fan you can blow air across stuff for quicker evaporation.