The finish needs to be dry but not cured for proper adhesion of the next coat. It is imperative to remove all residue between coats using a brush, tack cloth and vacuum. Also the finishing environment should be as dust free as possible. Any residue or dust which is on the surface will be entombed in the next coat. The second coat requires a little more care in brushing as it will probably lay on the surface.
Good strokes are important as is tipping off.
This will remove most bubbles and brush marks. The second coat and all others should be full strength unless the varnish you are using is very thick and does not flow out well. It is dependant on the varnish and should be thinned just enough to get good flow. After the second coat is dry, sand with 320 or 400 wet and dry sand paper dipped in water for a lubricant. I usually splash a little water on the surface when possible.