Do: Set your budget beforehand
It's a good idea that you establish your budget prior to beginning your artwork search.
Shipping costs could be thousands of dollars depending upon the scope of the work. Some
Outdoor sculptures and other works might require regular maintenance. Therefore, it is important to determine the potential costs of maintaining an art work.
Once you have decided on a price range you are comfortable with, start market research. There's plenty of art markets online
This page lists prices that have been published to give you an idea about the cost of each item. Artwork Archive’s Discovery platform, Artsy or Artspace can be explored.
1stDibs and Platform are just a couple of examples.
Do not ask for an offensive discount or attempt to get rid of the gallery.
You can negotiate prices up to a point.
Museums and major collectors typically receive a 20% discount. A lot of haggling can be an indication of a negative character and could lead to your being dismissed.
Not-sales" list if your tactics are too aggressive or plain rude.
By extension, don't attempt to circumvent a gallerist and purchase directly from the artist they represent. This puts the artist in a horrible position.