Appraising art is a little like restoration. It is good to know a little about how to get the information you need, but you should really leave the formal appraisal to an expert on the particular artist, period, style or region. You usually can get price information on a known artist if they have an auction record. If an artist does not have an auction record, but they have traceable sales through a gallery, you will have your work cut out for you.
Even if you are able to find prices for similar work, unless you are very familiar with the artists work, you can only give a range of value. Not all work created by an artist of the same size and subject will have the same value. Artists have good days and bad. In addition, the value of art can be cyclical. An artist who was hot 10 years ago, or sold at auction at the peak of the market may not bring the same money today. Often, it depends on who shows up at the auction. I would look for consistent sales.
I am no expert, but I do know there is an awful lot to learn on this subject. Can you recognize a forgery? I am familiar with several artists work, and I like to think I can recognize a good authentic work, but when it comes to appraisals or authentication, I try to refer to the experts.
Below are a few links that may help get you some basic auction records and biographical information about an artist. There are a lot of great books and a couple of subscription based Internet businesses that are good references for prices, biographical information, and even some visual references. But, be careful what you tell a client a painting may be worth.
Artprice.com (Internet reference)
Askart.com (Internet reference - American artists)
DealersChoiceBooks.com (reference books & CDs)