A skim coat
A thin skim over existing plaster or plasterboard usually dries in around a week in a warm, ventilated room. Cold, damp weather can double that.
A full re-plaster
Where a backing coat goes on first, there is far more water in the wall. Allow several weeks before decorating, longer on thick coats or in winter.
How to tell it's dry
Fresh plaster is dark pink or brown. As it dries it turns an even pale pink. Darker patches mean those areas are still wet, so wait until the whole wall is one colour.
Help it dry, don't force it
Open windows and keep the room at a steady, normal temperature. Don't point heaters or dehumidifiers straight at new plaster. Drying it too fast can cause cracking.
Painting new plaster
Start with a mist coat: trade matt emulsion thinned with water so it soaks in and seals the surface. Avoid vinyl or wipeable paints for the first coat, as they can peel off fresh plaster. Then paint as normal.