On XBox it'll be a PITA as you can't copy/paste, but in a nutshell:.. really want to help out with submitting distances ..
1. Log in to EDSM and open the page of the system you're in at the moment. Eg, "Beagle Point"
(It's better from an obscure system, ideally far away from one of the really popular systems)
2. Click on the "Distances" tab.
3. Click on "Generate needed distances" or "Generate featured systems"
4. Open the Galaxy Map in-game
5. For each system in the "Distance To" column, type in the name of the system, wait for the Galaxy Map to scroll to it, then enter the distance in the "ls (in Ly)?" column
6. Click "Submit new distances"