Well, I usually get my art from either deviantart or furaffinity. Deviantart has got "all kinds of art", while Furaffinity is pretty much only furry stuff and usually easier to find great furry artists on (Not that there aren't any good ones on dA, they're usually a bit trickier to find over there imo)
Many artists take commissions and usually have it written on their profiles, so it's quite easy to find people who do art for others, usually for a price.
The way I've done it have usually been to just browse the front page on FA to see if anyone's art catches my fancy, and if I see a style I like I go check that artists gallery for more examples of what they do, and their profile to see if they take commissions, and if their price list is affordable enough for me in that case. If they do, their prices are "right" for me, and I have an idea I think would fit their style, I send them a note asking if they've got any open slots and a short description of what I'd like.
