While creatures may choose to delay actions, it is not possible to time actions with others perfectly. Thus, any delay, that is, not starting an action on segment 1, will add a random 1d6 segments to any action.
Likewise, if waiting for a triggering event, when it occurs, the actor will add 1d6 segments before their readied action occurs (and that action is bound to take some time).
Thus, it is difficult to “shoot the spell caster with an arrow if they cast a spell” as there will be a 1d6 segment delay added to the speed factor of the missile weapon before the shot occurs.
Changing an action. See Combat Actions, Changing an Action. This may be announced by a figure at the beginning of any segment. This will create a delay.
If any condition—stunning, sleeping, held, whatever—restricts a creature from making a declaration until after the round starts, that creature will also suffer a delay (+1d6 segments added prior to their action beginning).
Player Discussion. Any discussion during the declaration phase of combat will introduce a delay in activity. The DM may assign this as a fixed number or random using the method above. Any tactical discussion between players during the round will likewise introduce delays unless a character is making a short statement or shouted warning (and this pertains to elements of the encounter they can see clearly; “Meta-gaming” is a disease).