This gives a nice overview:
https://www.youtube.com/watch?v=hXXe7422OYE (official FDev "pilots training" video).
As others already mentioned:
You need a bit of keybindings.
Then you need to be in super cruise with throttle at 0%.
Press the button to activate the FSS.
Press the button to make the initial honk - energy pulse to establish the orbital plane and find all the things in the system. Those found things will be shown as "blue blobs".
Now you adjust the frequency spectral thingy at the bottom to the desired setting and look around for blue blobs. If the frequency set below matches the object, then the blue blob will have a white solid circle - otherwise it's a white dotted circle. It might require a bit of aiming, but not that much.
Now press the zoom button. If the blue blob is an USS or a planet/moon you will have now scanned it and got all information the FSS will give you.
If it is a planet-moon system, then you will get presented more blue blobs on their orbit around the main blue blob. Adjust the frequency accordingly and zoom in on every blue blob.
The FSS will show you where frequencies are - so just select on and then move around and zoom in on white solid circle blue blobs until that frequency is marked as resolved (no wave pattern anymore). Go on to the next frequency wave pattern.