Ultimately this depends on how much of the project has been taken care of by you or other 'non artists.' Meaning that the answer if you've already built a game and need art to replace your temp graphics is different than if you've already created an engine and now wish to have someone help you write the story, create the characters and setting, and create art assets for those things inside the confines of your engine; is different than if you don't have anything created and only have a vague idea of how the gameplay should work and what kind of game you are making.
I have a completed game, but need replacement art assets.
Start by collecting a complete registry of the needed assets, organized by type: character sprites, interface components, tooltip icons, so on. And then sub-organized by other groupings as makes sense, UI elements can be ordered by what interface they are a part of, character sprite animations for all the motions can go under the character itself.
Being organized like this makes it very easy to track what has been completed percentage wise, and it also makes it very easy for an artist to swoop in and work on a section of the project and complete all the parts needed.
If tom'kin the barbarian needs walk, run, slide, jump, bash, big-bash, and super-bash animations; the artist will see all of this and be able to use the temp-art as a starting point to complete all of his animations.
I have an engine but nothing more.
Since you have an understanding of what kind of game you are making, be it a Shmup or RPG or RTS, you can write that down. Take stock of example game design documents around the web and use those as a starting point to detail the needed components of your game. RPGs will need items and characters and quests and such, for example. You know what items are in your engine, you know that they need a name, a description, an icon, and whatever else they need and the specifications of each. Write that down.
If you have an idea for the plot of the game, write that into the design doc. If you have an idea for the art, provide example images in the design doc.
Turn this document over to your artist/writer and let them have time with it. Then start working on a story and art bible. The story bible should ultimately contain the entire major plot of the game, including any branches. The art bible will start with concept art and eventually feature completed sketches of all the characters and settings in the game. It isn't required to put everything in these bibles, but the more the better.
After you are happy with these three documents, produce your game with temp art as the artist/writer starts putting together the assets. Create a list like in the sections above and replace the temp art as you go.
I have nothing, what first?
Play lots of games in the style/genre you want. Collect screenshots and videos if you can. Meet with your game designer and discuss what kind of game you want to make and the kinds of technology you have available. Do you know how to program 3D games? 2D? Have you made mostly RPGs? Roguelikes? Shmups? Puzzle games?
Before long an idea will gel between you. Then the game designer can go off and put together a design document shell. Discuss again what your options are, show some demonstration code you put together since the last time you met, and make sure you are both on the same page. Iterate. Eventually you'll be able to pick up with the section above, and then move on to the top section and you are done.