Cobblestone driveways are washed depending on the material which the stones are seated into - sand, soil, or concrete.
Sand - The pavers will need to have the sand brushed back into the cracks if they become loose and generally swept to keep the sand between and beneath the pavers instead of falling out.
Soil - To clean weeds between cobblestones embedded in soil you can either use weed killer or you can plant hardy ground covers. Ground covers grow in between the cobblestones to control both erosion and weeds while withstanding heavy traffic.
Concrete - A pressure washer can be used and the cobbles can be cleaned just like concrete.