You can move the background the same way as any other sprite, it's just a matter of calculating the coordinates. If the player should move right, then instead, the background sprite should move the same amount to the left. (Negative X coordinates are possible to slide it partly off-screen.)
There is only one catch. If your background is the same size as the screen, then part of the screen will be black as the background slides out of view. (This is not a problem if the background picture is larger than the screen but then the image consumes more memory as well, of course.) You can solve this in two ways.
One solution is to make two copies of the background sprite and move them in sync. As one copy slides out to the left, the other copy slides in from the right. (The two pictures must join seamlessly at the sides.)
The other solution is to apply texture scrolling. Then the sprite does not move at all, but the texture is drawn onto the sprite at different positions. One copy of the picture is enough but calculating the rotation amount can be a bit tricky. (Again, the two edges of the picture must join smoothly.)
If you have more than one sprite for background - so that the background is made of tiles - then you have to move all of them.
For an example of both tile moving and texture scrolling, have a look at my side-scroller demo, which is attached as a zip file to one of my posts in page 3 of the Dark GDK coding challenges thread.
http://forum.thegamecreators.com/?m=forum_view&t=150933&b=22&p=2
