How? Definitions I can find are all similar to this:

Separating the art from the artist is a known concept defined as a manner to discern people’s appreciation of an artist’s work from their hate for the creator’s actions or opinions.

Source

That is all. Consuming the art and appreciating it no matter who created it. This doesn’t mean it has to be purchased. The idea is simply that you don’t have to say, burn Rowling’s books that you have purchased once upon a time as mentioned in the opinion article. Or delete some artist’s music from your music player, put movie DVDs into microwave oven, delete all photos of a certain painting, etc…