Ok, the best way we have found which is very profitable as some missions will stack (killing one skimmer may count towards more than one contract if you have more than one contract or “stack” them.) is as follows.
As per @komemiute 's video, you could attack the base assigned. But we found you will get the penalty or fine for trespassing and on higher paid missions even security vessels. We found it best not to attack assigned base.
So this is what we do.
Fly to the base/planet assigned to be in general area. Then move away from base and search for POI’s (points of interest). IIRC poi’s show up on the scanner as a blue circle when you are above 2klm from the surface.
So fly around until you spot the blue circle
Try to put yourself roughly in the middle of the circle then land straight down. Look about as you head down as you may pick up a site with skimmers visually.
Get in rover and use wave scanner to find various areas that may be protected by skimmers. Just be warned though, some sites may have a ship somewhere near. Don’t attack the skimmers, if there is a landed ship nearby. It will attack you. Just move on to another site.
Each point of interest (blue circle) holds multiple sites. Usually a minimum of 4 and i have had up to 7-8 depending on how easy they are to find with wave scanner.
You must be inside a POI
Check out my wave scanner tutorial