Unlike a violin, where intonation ios determined by left had finger positions, On a guitar, intonation is largely controlled by the positioning of the frets relative to each other and to the bridge. To a limited extent, intonation can be altered by, say, pressing down too hard on a given fret and taking the pitch sharp. In non-classical music of course, (blues for example), players bend the pitch by pulling or pushing the string to one side. That doesn't work too well on classical guitar and I've never seen or heard any classical guitar music that employs it.
So provided your left hand technique is good, all you have to worry about is correct fret positioning and height of the action. Generally you want this to be as low as possible without buzzing.
Look along the fingerboard from the nut end to see if it is dead straight. For a classical instrument there should be no perceptible curve, either concave or convex - either lengthwise or across.
Next test the octave of each open string.
Play the harmonic at the 12th fret and compare with the fretted note at the twelfth fret. The pitch should be identical. If it isn't then either (a) the bridge is in the wrong place, (b) the action is way too high or (c) the string is not perfect. Nylon strings in particular are susceptible to not having precise diameter along their length. The G-string tends to be the worst. If the guitar has cheap strings, it is very difficult to check the intonation of the guitar.
Make sure the guitar is tuned to concert pitch. If the strings are too tight, the neck will lift and if they are too loose, you may get buzzing.
Because the instrument is tuned to concert pitch you can use a clip-on electronic tuner to check as many frets as you care to.
Remember that a guitar is an equal temperament instrument. https://en.wikipedia.org/wiki/Equal_temperament
This makes the guitar difficult to tune 'perfectly'. The problem with the standard tuning method (fifth fret against open string except for 2 and 3), is that it creates problems with thirds (for example the major third on the 1st string when playing a D-chord can sound sharp.
Because you are using concert pitch, if you have a lot of patience, you can work your way up each string a fret at a time an check every single one against the tuner. Note that all but specialist tuners use Equal Temperament.
I hope that answers some of what you were asking.