Mat and frame all of your two dimensional artwork for display.
Install hangers on the back of the frames so that they can be hung securely from gallery walls.
Take high resolution photos of all of your best work and save them to a disk to serve as a digital portfolio.
Make tags for your pieces that list its title, your name, the media used, the date created, and how much you want for it.
Attach the tags securely to the backs of your artwork to make it easier for the galleries to label your work.
Look for co-op galleries, which allow the artist to rent gallery space to display and sell their work, and representational galleries, which usually require a higher commission, but provide more exposure and promotion.
Contact the galleries you are interested in with a copy of your digital portfolio to see if they are willing to display your art.
Transport your artwork to the gallery very carefully if they have agreed to show it.
Promote your display as much as possible while it is featured in the gallery.