Textures don't appear when I render

Okay, first time with blender. I have created and unwrapped a mesh for painting and have been happily painting the UV map using the texture paint tool in the UV/Image editor window, but while the textures are coming up in the 3D view, when I render using F12 I don’t get anything but the same old boring grey mesh. No sign of any texture. What am I missing?

Sorry, I just figured it out. I still have to actually create a new image texture and apply it.

Great! But I’m having trouble understanding how Blender does that too. Care to elaborate?