There are several structures (ying) we can break - i.e. render ineffective - hand structure (sau ying), kick structure (gerk ying), or stance structure (ma ying), or body unity (yu-ma-sau ying). Methods of breaking structure involve unlinking an element or elements in body unity (joints) and/or disrupting the opponent's Center of Gravity (CoG). Either avoiding (moving off the line of attack - often by juen ma - which in the fashion in which we do it does not just realign facing but also shifts the centerline), and/or redirecting the opponent's line of attack would seem an integral initial component of breaking structure. This can occur at different points in the time/space continuum of attack (initial, medial, almost terminal - further away, half way there, almost there) - deflecting and/or intercepting earlier or later - it may be contingent to varying degrees on the observation/knowledge/intuition of the opponent's skills, speed etc or it may simply be circumstantial.
To categorise breaking structure I'd think it is broken by uprooting and this can be done by:
(i) rotation (either pushing/pulling him or you using juen ma - thus turning the centerline);
(ii) direct rearward force; or
(iii) force applied diagonally forwards (pulling) or backwards across the opponent (pushing). Our ideal is to ensure the opponent's shoulder is significantly displaced from vertical alignment with the hip and/or his pelvis displaced so as to ensure the vertical alignment of the shoulder(s) is significantly behind the heel(s) or significantly displaced in front of the toes of both feet if in YJKYM, or his attacking limb obscures and excludes the other limb.
Ideally we will also take the shoulders off front-facing alignment if they are facing forwards - many attackers advance one shoulder helping us in this task. We should always attempt to disrupt the opponent's psychological focus to divide his attention away from attack or defence/attack to defend/maintain balance/structure. We should attempt to express force where the opponent cannot resist - at the terminus of the limb levers (wrist/ankle) (jerk-pull) or at the central joints (elbow/knee) (push) - not confronting the opponent's force but meeting it ideally at approximately a 45 or 90 degree angle - ideally this will force the attacking limb across the bodyline/centerline and disrupt the CoG. As this occurs step deep into the opponent's space - forward step going between his legs - sometimes as it drops from a kick attack - or with your shin locking his or your ankle/foot locking his as you step behind his foot - thus putting his base out of alignment or locking it so it cannot readjust balance. Sometimes you can use your bodyweight if you can do so without sacrificing the vertical alignment of your spine.
An obvious component to breaking structure - however defined is to attack the attack and to thereby cause such pain that it divides the opponent's focus of attention and disrupts intent - as the brain blinks** you have struck your target and he has not registered it during the blink. If you train diligently and correctly for a long time, then one day something truly marvellous happens!
** Zopa acknowledges his friend Robert Redenbach, international security consultant, as the originator of this excellent term.