It's a bit complicated because the design is pretty bad - but basically you need to set a keybind to "next fire group", then set up a fire group for your discovery scanner. After that you can choose then "fire" the scanner instead of your lasers after you reach a system, and it should hopefully find more "astronomical objects" (which show as unexplored in the navigation tab) at which point you can go visit them to scan further, making more cash.
It's ridiculously complicated to even explain in writing, which is why I knew it would make a good video. The game UI is very, very old-school and is probably the #1 issue that new and younger players will have with the game, imo.