Right now I am thinking of it like a typewriter. When the head gets to the end, it jumps back to the first position and repeats that. Am I clos?
You are definitely on the right track. Basically, you draw your background twice.
So you have two instances of your background: A and B. As background A moves along you draw background B trailing behind it right behind it. Then when background A completely passes your screen threshold you can "jump" background A back to its starting position and background B should then follow. Jumping right behind, creating a endless scrolling effect.
Microsoft has an example article using their XNA framework, which should be super easy to get going in whatever framework you are working in