Research the gallery. Google them and find out all you can about them. First of all, are they a fit for your art? If you are doing anime and they do high-end corporate paintings. Stop there. If they feature national artists and you have never had your art in a gallery before, maybe not the best for you. If they have local artists and you do oil painting of historic local buildings, maybe there is a chance.
Research the gallery some more. During your research see what they sell their paintings for, how they market and check out their reputation. Are they on Facebook or other social media. Read their posts to find out more and follow them for a while.
Stop by and visit. But do it as a visitor not as an artist. Don’t walk in and just ask if they will carry your art. Talking to other galleries, they all agree, an instant turn-off is a person walking in and just asking, “Are you adding artists?” or “Can I add my art to your gallery?” It’s like walking into a business and saying “Will you hire me?”
If you think that your art might be good enough for the gallery then approach the gallery via email. Introduce yourself with a short bio and some good pictures of your art. Or ask to make an appointment to bring in some samples of your work. Never just walk in with samples. And pictures on a cell phone are not a good representation of your work. A simple bio, as mentioned before, printed out would be nice to have also if you have a history.
Take your time to get to know them. Go to their shows or exhibits. I know an artist that went to a gallery’s shows every month. She got to know the owners, commented on their art and became friends. It was only then that she mentions, rather casually, that she was a metal artist. “Oh, really? We’d love to see your work!” Smooth.
As a new artist it can be boost to the ego when someone asks you to do a commission. They usually don’t use that word in their request but it is inferred. “I love your artwork! Can you paint my dog?”