There is no precise definition of a double star.
We could state that a double star appears as a single star to the naked eye or even binoculars but appears as two stars in a telescope on higher power.
However, many double stars are not even visible naked eye nor in binoculars.
Many fainter and fainter stars are now being classified as components of double stars.
To what magnitude do we go? Especially if it is likely that they are simply in the same line of sight.
We could state that a double star is a pair of stars closer than so many arc seconds (say 200").
But then we have something like the epsilon Lyrae "Double Double", each double being 211" apart but part of the same system.
So how far out do we go?
And what about stars in a cluster? We don't normally classify the closer stars in a globular as multiple stars.
We certainly classify some close stars in open clusters as doubles e.g. DUN 206 in the core of NGC 6193.
We can say that observed (i.e. visual) binary stars are double stars.
Relative to the number of catalogued multiple stars very few have orbital elements i.e. a known period of orbit described as an ellipse.
Known binary stars usually have a relatively fast orbital period ( less than a few hundred years). So orbits have been observed or at least extrapolated.
How many have periods of the order of 10000 to 100000 years or more?
In any case, the vast majority of doubles have just not been studied closely enough. There are too many of them.
Many multiple stars might be just travelling through space together with no observed orbital rotation.
For brighter stars, it is usually not until you get a few hundred arc seconds away that the secondary components might start intermixing with other background or foreground stars.
If the components of a double star are within 50 arc seconds or even 100 arc seconds of each other, the brighter components are usually quite easy to identify.
Where spectral types are known, you can also use colour to identify some of the stars e.g. G5 is yellow, A4 is white, K3 is orange etc.
Example: Albireo has obvious orange A and blue B components.
Identification of A and B components becomes trickier where magnitudes and spectral classes are similar.
For a multiple star of three or more components, it might not be clear which is the A, B, C, etc components.
Often, the difference in magnitude and the separations will identify the brighter and dimmer stars, the closer and wider stars.
Failing this you fall back to the PA (position angle). This measure is given as an angle from the primary, anti-clockwise from celestial north.
It is often not necessary to know the exact direction of celestial north but simply the relative positions of the component stars.
For double star data, go to this site
Select Browse this table… at top left.
If you just want current simple data-
Untick the boxes pa date1, first date, class in the step 3 table.
Then tick the boxes pa date2, separation date2, comp1 mag, comp2 mag
As an example-
Enter gam vel into the Object Name at 4.
Then simply Start Search.
For gamma Velorum ABCD, magnitudes are 1.8, 4.1, 7.3, 9.4 rounded to one decimal place.
Separations and PAs are AB 40" and 221 degrees, AC 62" and 152 degrees, AD 94" and 142 degrees.
Using a 360 degree protractor you can plot these as shown in the attached diagram.
The stars form an obvious Y asterism and can be easily identified.