How should varnish be applied? There are probably several ways, including simply spraying it on. The traditional way that virtually guarantees a good result is to do it with a brush. I have several hog bristle brushes for oil and several synthetics for acrylic that I reserve for varnishing, so that there is never any pigment residue in the varnish brush. I apply acrylic varnish the same way that I apply Damar varnish to an oil.
If the painting is an oil, first check the surface to see whether some parts look very dry or matte. Just varnishing may not resolve this issue, since the varnish can just sink into the matte portions of the painting. The solution is to brush linseed oil or a medium like Liquin into the matte places and rub the excess off with a cloth. When the application has dried, then apply the final re-dissolvable varnish. Typically, the final varnish should only be applied after the painting has dried for several months. If the paint has been applied thickly, six months. (The reason for waiting is that oil paints dry by oxidization and a final varnish that prevents contact between the paint and the air will interfere with the drying process.)
If the painting is an acrylic, some painters will apply two different varnish coats, first a clear acrylic coat that provides an isolation layer over the paint. Given the rapid drying time of acrylics, varnish can be applied after several hours in the case of thinly applied paint or after an interval ranging from several days to a few weeks in the case of more thickly applied paint. This layer will not re-dissolve. After it dries thoroughly, a coat of re-dissolvable or removable varnish can be applied.
When applying varnish, I begin in the upper left and varnish a square portion about 6-8 inches, brushing first horizontally and then vertically. Then I work across the top, in a series 6-8 inch squares, blending the edge of each new square into the previous, repeating the process all the way across the canvas. When I get to the far right, I move down to the next unvarnished section on the left and work across, again in 6-8 inch squares, etc., until the whole canvas is covered. I try to apply the varnish evenly and thinly. It is also better to apply two thin coats of varnish than one thick one. While the varnish is still wet, I look at the entire canvas at an angle to see if I have missed any spots. Usually the technique of brushing first horizontally and then vertically covers very well. On a really big painting I might increase the size of the squares. On a really small painting, I do the whole thing at once.
When finished applying the varnish, lay the canvas flat, so that the varnish does not run or drip, in a dust free area.