First go to Biography in Context to see if there is post on the artist. Some artists will have more information than others.
Then go to Google for an online search on the artist. The artist below is not longer living, so she doesn't have an artist page. You'll have to dig a bit more to find information. A few suggestions: big museum websites, and the reference list on Wikipedia.
Below is a listing of other sources for Ana Mendieta from Wikipedia. Go to the direct sites for help.
If the artist is very contemporary (still alive and working), chances are you'll find their artist page but you might not find them in Biography in Context. That's okay! Use their artist page, museum pages, and online videos to research them.