Join online forums if you want to collect furry art. The bulk of furry art is found online at sites like DeviantART and VLC Furry Art. Be warned that most online furry sites have strong adult themes that may challenge your sensibilities.
Download pictures from online artist communities, such as those mentioned in Step 1. Many furry artists make their artwork available for free, provided you don't reproduce it in any way. You can build your furry art collection quite quickly this way.
Purchase furry art pictures online at artists' sites. Nearly all successful commercial furry art sites are adult in nature, and some of them are quite graphic. Artists make their adult furry artwork available for purchase via credit card.
Commission custom furry art from artists whose work strongly appeals to you. The cost of purchasing custom artwork varies widely, but this type of art is generally considerably less expensive than the art you may find in other, more traditional, artist circles.
Buy prints of furry artwork you enjoy to build your collection. Many furry artists create their original work on paper and then scan it into a computer. Others sketch out a drawing on paper and create the finished work on a computer. They may then make the sketch available for purchase.