Say I'm a programmer who has done his own sprites or 3d models which would fall into programmer-ish kind of art. What steps can I take in order to improve or replace my own art?
1) If you want to improve try putting up your work on specialized sites like http://www.polycount.com/forum/
2) If you don't have time or insert reason here go to recruiting sites, here are a few to get you started:
http://opengameart.org/ its a nice resource too.
The best way of having your programmer art replaced by real art is to carry on making a great game.
Pimp your game as often as you can - concentrate of game mechanics first - then I am sure that you'll attract some artist types - maybe even for free (join the team).
This approach is probably the only one if you're short of cash, and/or want to stay free.
Programmers art could make sure that you concentrate on the most important aspect of your game: the game itself.
There are of course places where you can grab models and art under an open license, but I would just carry on making a game if I were you.
Don't bother spending too much time trying to learn how to be an artist yourself.
That skill takes years..
You could try making more art. The saying 'practice makes perfect' is probably applicable here.
Or, you could advertise on a site such as Gamedev's Help Wanted Forum for an artist, saying that you've created such and such a game, with your programmer art, and looking for a improvment to the graphical quality.
The other way is to get free images, textures, and models from many sites on the internet. However, these aren't necessarily what you want. Option 2 is probably the best way, unless it's more of a learning project (not for release).
I would recommend you to search a skinner and/or 2D Artist who is skilled and can create that kind of art. This is a good forum i remember, where like just skilled artists are grouped :) You could search at Deviantart too, but there it's imo more complicated.
Or you try learning it in a professional way, but that is exhausting...
Go to forums. Artists need you as much as you need them.