How do I open an exported map???

Files downloaded from the "Export" option are in OpenStreetMap XML format (often known as ".osm"). You will need specialist software to use these files. If you explain what it is you actually want to do with the map data, and what sort of computer you use, we can perhaps recommend some such software.

If you just want to save an image file (e.g. PNG, JPEG or PDF), then you should use the "Share" button on the right-hand side of the map rather than the "Export" tab.