First, it must be established what is needed to remove the varnish. It is usually stated on the varnish bottle what is needed to remove it but bear in mind that some varnishes are non-removable eg. craft/acrylic varnish.
Start by testing a discreet corner of the painting- a part that is covered by the frame, for example. Use a lint-free cloth dipped in the mineral solvent or varnish remover and gently rub the surface of the painting. Stop if colour starts to come off on the cloth. Work methodically, removing one small square at a time. When the cloth gets dirty, replace it with a clean one so you don’t spread the old varnish across the painting.