Sometimes artists sell pieces ready framed. Other times, unframed. Canvasses can often be hung unframed, if you so choose. However, framing does offer the artwork some protection. If the piece you are choosing is unframed, ask the artist for their suggestions – some do their own framing, and those who don't can probably recommend at least one great framer.
When it comes to a frame, your budget is of course a consideration. Beyond that though, you'll want to choose a frame that highlights the work, and doesn't 'box it in' or compete with it. Take a look at the colours in the work. Some of the colours that appear in smaller areas of the work may be a great choice for the matting or frame. The texture, finish, and thickness/width of the frame also influence the final look - I've got at least a couple of framed paintings at home where the texture and finish of the frame are similar, though not the same, to textures in the painting. Examples could include paintings with straw, wood, or grassy textures, or watery, rippled textures, or worn, crackled textures. This is where the artist or framer's eye can really help. Choosing something that works with the piece will give much better results than simply matching the furniture.
