The first thing you need to do before copying many map into OpenStreetMap is check the licence. If importing data the import guidelines need to be followed. I know this is boring, but the data needs to be acceptable for worldwide use without legal issues.
If you have a map layer that is just images, you normally need to find a way to add that imagery to the editor you are using as a background layer. The way to do this depends on the software you use and the way the map images are served, the most common formats are probably WMS and TMS.