Artistic cooperatives function very much like other types of co-ops. However, they limit their members to artists.
Often, an artist's co-op also has goals beyond just providing a living and working space for the artists involved. It may also serve as a business that can help artists buy materials important to their craft (like matting supplies or high ticket items like a printing press). In some cases, the co-op may also be designed to serve as an occasional gallery for the artists' work through shows and other displays.
A co-op for artists can be wonderful -- or a miserable failure. To make yours succeed, you need to approach it from the start as a business. With that in mind, here are some tips:
Choose your location carefully. Think of your location as an investment. The cheapest place to buy a co-op is not likely to be the easiest place to attract potential customers when you have gallery events.
Put someone in charge of directing the show and delegating tasks. Pick three people who are detail-oriented and business-minded to serve as directors. Don't try to run the entire co-op by popular vote or you'll get bogged down on every detail.
Be discerning. While it's nice to think that every artist is of equal value, the reality is that some artists are just not at the same level as others. Establish an interview process before you allow a new artist to buy-in to the co-op so that you don't ruin your co-ops reputation for excellence.
Finally, consider getting some legal assistance when you go through the formal process of setting up the co-op. You don't want a simple mistake made in the early days of your formation to cause major problems later.