Old School Ways to learn about the artist and their work:
1. Look through books, catalogs, articles and reviews about the artist - as many as you can find and from as many different sources as possible.
2. Talk with collectors who are familiar with the artist, dealers who deal in the artist, and even curators or critics - whenever and wherever you can. Ask them what makes the good art good.
3. Shop around. Get multiple opinions from multiple dealers before you buy. Do not settle exclusively on 1 dealer until you have a good feel for the overall market.4. Don't try to get bargains until you know what you are doing.
More modern ways to learn about the artist and their work, especially indie artists:
1. Go online! Find the artist's website or blog and read up on them. See where they have shown and where their art hangs and get an overall feel of their art.
2. Check out feedback on their etsy or eBay or look for testimonials or guest books on their website to see what people had to say about their art.
3. If they are independent you don't have to shop around! You can just purchase directly from the artist.
4. Don't try to get bargains at all. The artist will likely bring you into their inner circle and you will no doubt get all kinds of special privileges like hearing about their new works first, being invited to openings, etc.