Most people do their laundry at a laundromat like anyone who doesn't own a washer/dryer. It's not that bad:

1. put your clothes in the washer
2. set a timer and go back to the van. Connect to the wifi. Chill
3. when the timer goes off put your clothes in the dryer
4. set a timer…

The only real pro tip here is to bring your own detergent; buying it at the laundromat is very expensive.

A common off-grid clothes washing solution is a bucket with a laundry plunger. These plungers differ from toilet plungers because their design forces water back-and-forth through the laundry.
Demonstration (youtube)

A regular broom handle will screw into the plunger, allowing standing operation.

Scrubba and similar camping wash bags work by filling with clothes and washwater. As the hiker walks or van moves the water sloshes around and cleans the clothes.