Problem is, if you ask them on the phone as they suggest, they will always say no! So you need to get your work across their desk first - mention a mutual contact/collector; or the last art prize you were selected for; or where you trained, how long you have been painting etc. I have exhibited in three states, and each of these galleries asked me to show them my work after engaging them in discussions about the current exhibition/artist; or having seen my work elsewhere (an art fair, another gallery). So get out there and talk to the galleries (you may not like the dealer even if you like their stable - and, let me tell you, that makes for a rough ride) and get your work out there as much as possible (artist run initiatives, Fairs, art prizes; personally funded group shows). The targeted approach is necessary to know which galleries to have these discussions with (natural conversation flows due to your interest in their artist)
I also recommend starting with a list of favourite galleries (whose stable you think your work would suit), begin at your top, -aim high! approaching one gallery a time. At worst, the galleries will have now seen your work and would recognise it - say as judges at Art Prizes in the future. Wait for a response, and after rejection (and licking your wounds, keep trying and, most of all, keep painting. As the "rejecting" galleries have told me, hard work, dedication and persistence will pay off! What are your tips for approaching a gallery? Post your comments here.