How do I get art galleries to show some of my drawings?>?

Answer 1

Put together a strong portfolio of your work and start making the palm sweating trips to meet with the curators and/or owners.
Bring your own white gloves and business cards.
Burn some images to a CD to leave with them even if they tell you to go away. Keep at them with your new work.
Cafes always need wall space filled and love work from local artists. Approach the managers/owners with a smaller portfolio of work. They have less time to look at your large gallery book and cafes are messy.
Have some of your work matted, glass and framed and ready to hang at a moments notice. Don't choose colored frames or huge ones. Use a thin brushed aluminum frame that wont light up too shiny.
Buy a small level, measuring tape and a good amount of hanging wire and assortment of wall mounts, small finishing nails and a small hammer for hanging your work in cafes, restaurants, banks, offices, smaller collective galleries etc.

Answer 2

Ask them they are always very receptive.Take 2-3 paintings / drawings to show them your work and try to negotiate terms with them.