A standard five gallon bucket and plunger will work. I have used this setup for extremely dirty work clothes and get good results.

I helps if you keep the load sizes small, use about a quarter the detergent you would in a standard sized washer, and dissolve the detergent into the water before adding the clothes. Two loads does a pair of jeans, a long-sleeved work shirt, two tee shirts, a couple of pairs of underwear and two pairs of socks. It takes about an hour and can be done while you watch TV.

Using a plunger I work one edge in a semi-circular pattern so the clothes roll over and they all get some action. The stroke is fast-in-slow-out as this keeps the clothes moving and suspended in the water. As opposed to beat down in the bottom.

I agitate for fifteen minutes, empty, wring out the bulk of the water, add water, work it for ten minutes more, wring and hang to dry.

A roller wringer or mop press makes the whole process less tiring. Wringing out jeans by hand gets to be like work. In fact when I had access to one I sometimes used the mop bucket and wringer setup. The bucket is a bit larger and the wringer is a plus.