How are X and Y defined in DirectX?

X and Y aren't strictly defined in any particular way, and you can have them work any way you wish. It all depends on the projection matrix you set up, and that can use either left-handed coords (using the D3DX -LH functions, for example), right handed coords (-RH functions), or be any custom matrix you wish. The only exception to this is if you supply pretransformed coords (equivalent to D3DFVF_XYZRHW in the old fixed pipeline), in which case top-left is 0,0 and positions increase as you move towards bottom-right.

mhagain is right.

But what makes me wonder is how did you come to the assumption that in Direct3D by default the +X goes left?
If we were to discuss the "default" axes orientation, then it would rather be +X pointing right, +Y up and +Z into the screen (or from the screen with RH), because this orientation is suggested also by the transformed vertices (view space, screen space etc). And last but not least, this: http://msdn.microsoft.com/en-us/library/bb204853%28v=vs.85%29.aspx

To sum it up: it all depends on you (on your definition of the view and proj matrices), as mhagain said.
But the somehow "default" orientation is +X right and -X left, not as you said.

I've been using LH functions, evidently. I don't think I know enough about it to risk a change, this late in the project.
Thanks for the pointers guys. I didn't even know what to search for originally.