The first step is to observe the aplombs at rest, and on flat ground. The best is in front of a wall, which helps to observe the contours of the limbs. Small trick, a dark wall is more convenient if the horse has a clear colors. This technique allows you to see if your horse is standing on the front, calf-kneed, base-narrow conformation, base-wide conformation, ....
Afterwards, you have the technique or you make your horse walk (you must not observe them after a session). For this method of observation, you must make him walk and trotter by making the return, without it having nothing on him (cover, saddle, ...) and on a hard and flat ground. An outside person must observe next to your horse. You have to observe the irregularities in the stride, if there is an embarrassment, a lameness, or if he hesitates to put the paw.
On horseback, it is mainly a question of feeling, for example if your horse takes more time to set out than usual, if it is irregular in its stride, its amplitudes vary without reason and without you ask . There is also his attitude; If your horse stumbles, or if he has the lower neck, or even a back pain.
I hope this helps, bye.
I've found that a combination of bending exercises, and extending/collecting work really help to improve straightness. A general feeling of straightness is when you don't feel your horse leaning on either leg or either rein. They will not feel laggy to your aids, and you will get the feeling that they are working right under you, not behind, in front, or bowed out in any direction.
Ask for inside and outside bend on both reins, you can alternate 4-8 strides of extension and collection in a gate, serpentines, and changes of rein will all help you to get there!