Before selling a work of art you consider of some value, it is a good idea to get it authenticated first, so you know for sure whether you are selling a copy or the original. For John T Fitzgerald, you may need an expert in Arizona art, or art of the American deserts.
It's difficult to know the value of your picture without looking at it, or knowing its size, condition, or the materials used. Fitzgerald's art also doesn't come up for sale often, so there is little online guidance available.
Ebay has two pieces from Fitzgerald on offer, one a simple pen and ink drawing of a cactus for $80.00, another a portrait of a Mexican man has a starting bid price of $200.00. The 'traditional' auction site invaluable.comnotes that a collection of 3 pieces of Fitzgerald art went under the hammer in 2011 in Scottsdale, Arizona, but will only reveal the price to members of that site.
There are online art communities you can turn to for assistance, if you join up, you can ask around for help in valuing you art. Two such sites aredart.fine-art.com and askart.com.
We can all enjoy art for the sake of it, but if you want to see how the rich and famous go about evaluating their collections, watch this YouTube film hosted by Forbes: