The most easy thing to handle which came to my mind is just to draw fullscreen quad with your background texture. And move UVs in x (so move only U). And set UV border method to repeat.
edit: Texture coords are between 0-1. But that doesn't mean that you cannot specify any other values. UV border method says how will gpu handle value beyond 1 and under 0. You can set it to clamp, mirror, repeat. In opengl you can do it this way:
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
nice article is here: http://www.flipcode.com/archives/Advanced_OpenGL_Texture_Mapping.shtml