You could do the search for something moving against the background thing but you need good eyesight and lots of patience.
This indeed, but note this first. Near a start, space is dark due to dust and other dark matter. Therefore, only the brightest stars are visible, or (and this is important) the most closest. Orange stars, red dwarfs, brown dwarfs and other faint stuff are almost always not visible when they are close neighbours (I don't mean compagnions) of the star you visit. When they are visible when you are near a star, then those are almost always close compagnions and theirfore the meat and potatoes your are after. Now do the thing Mikey2305 said, but do not fly directly to them, otherwise they won't move against the background. position them in the corner of your canopy and start to fly forward and keep an eye on them. Sometimes they are 40.000 LS (or even more) away, so be patient.
It takes a short while, but you'll get a nose for it. Above method almost never failed me.