you have to allow for the wall itself to dry. A brick wall dries at about one month per inch thickness. If it rains during build the wall may be thoroughly wet, so for a cavity wall, allow four months or so after the roof goes on.
Wet new plaster is chocolate brown, dry plaster is pale pink and you can apply a breathing paint like Supermatt, but even after that, moisture will be evaporating from the wall itself.
With an old dry wall that is being replastered, maybe a month.
If whiskers, bloom or crystals appear on the surface, that is efflorescence (mineral salts left behind by evaporating water) so brush them off (don't try to wash off) and wait until it has stopped.
Fresh air, not heat, dries walls, so open the windows. In an alcove or damp corner, put an ordinary domestic fan to blow moving air over the surface. It will dry out like a windy day dries washing.
If you want to know if moisture is coming off a wall (or floor) tape a piece of clear plastic tightly to it and see if condensation appears under the plastic after a few days.