Heres what you do when you want to know if theres anything for you to be the FIRST to discover in any new system you jump to.
First thing when you jump in is to hold down the discovery scanner and let it gather the system information.
It will pop up and tell you how many orbital paths it found for that system. The number it gives includes stars, asteroid belts and planets and moons in the system ie. If it just says '1 orbital path found', then it's JUST that single star in the system and theres nothing else to discover.
Any number bigger than 1, go to the next step.
Open the system map. If you see any planets next to the star, then someone has been there before you. The number of stars, asteroid belts, planets and moons should add up to the number of orbital paths that it found in the discovery scanner.
IF you run the discovery scanner and it pops up '20 orbital paths found', but when you go into the SYSTEM sceen, it shows ONLY the stars without any planets or anything, it means there are planets that NO ONE ELSE has found yet. If it only has a single star in the system screen, there will be 19 as yet undiscovered planets or whatever. You need to find them.
You find them by opening the FSS (Full Spectrum Scanner).
Slow down to min speed in supercruise. Open FSS. Scan around and look for when it shows stronger signals... err, at this point...look up a FSS guide.
As well - There are TWO discoveries to be made with each planet. You have the discovery part which anyone doing the FSS discovery will get, but if you actually go out and do a detailed surface scan of teh body, tahts a discovery in itself. The system screen shows who first discovered it, and who first mapped it.
ALSO - EVEN IF there ARE planets next to the star, it doesnt mean ALL the planets have been discovered. If it says it found 10 orbital bodies, but the system screen shows onlt the star and one planet, it means the first to be there didnt bother finding everything. You can...
BUT REMEMBER! - Nothing's official until you SELL all that collected universal cartography data, which can be done at most ports. You will likely be upset being blown up 2 minutes before docking... Everything will be lost in the flames.