How should I go about washing cotton clothing? Some of them are 95% cotton and some are only 80% cotton.

There should be washing instructions on the item but if not, warm soapy water and air dry. Heat can cause cotton to shrink but most modern cotton takes that into account by pre shrinking the item. If it's machine washable, shrinkage shouldn't be a problem.

Well, though it's a bit cringey, the less you wash a garment the better. I actually heard an interview with the president of Levi Strauss & Co in which he recommended you not wash your jeans. Washing deteriorates cotton clothes, so any way you avoid washing you should. That is unless you like the frayed and hole-ridden look, which actually is pretty fashionable these days.

BTW, I do wash my jeans, but I try to put it off as long as possible and never dry them in the dryer. Other cottons I just try to go easy with-- gentle cycle and all. I think electric dryers do the worst damage.

I ordered it off Amazon as it would be awkward to go into a clothes shop... Uh, you know.
No manufacturer's instructions. It's really soft clothing. You touch it and it feels really soft.

Air dry. I assume I hang it up and wait for it to dry.
Soap works for it? I didn't know that.
Um, I sleep in these, so it would get really, really stinky if I don't wash them.

The instructions could be on the size tag or in some underwear, printed on the inside. It's rare that something doesn't contain care instructions somewhere in the item. Soap or detergent will work. Soap was the only thing available until detergents were developed and you don't want to know what they used before soap was invented. Air drying was how everything was dried before the dryer became common. My family didn't own a dryer until I was in my teens. It became interesting in the winter when there was snow out side because my mom would bring the laundry in stiff as a board.

Wash in cold water and detergent. Most detergents today work in cold water. Also use the gentle cycle if necessary. When washed, hang to dry in a doorway with good airflow.

Cold water will not shrink especially if it is 100% cotton. 85% indicates there is some sort of synthetic blend added to the cotton. This will accept higher temps because the shrinkage is minimized. So it would not hurt much to wash in warm water once a month. But do air dry.