First, forget about the captains in the context of big army set-piece battles. Other than specialist scouts, miners or engineers, a unit the size of a modern squad or section is not going to be operating independently, they will only move and fight as part of a larger group. Which means that the real question is how long it will take for orders to get from a general to a centurion, probably via a commander.
Second, forget about giving meaningful orders to a unit that has already engaged the enemy in melee. Once a soldier is hacking and slashing, blocking and parrying against the enemies in front of him, with all the accompanying battlecries, shouting and screaming of the wounded and dying, there is no way that he is going to pay much attention to anything other than his piece of the battle. You can shout orders and blow trumpets and whatever you like, he's not going to care. The only thing he will notice is if the people on one or both sides of him start going down and not being replaced (or running), at which point he is likely to follow suit rather than dying in place.
Which means that the units that can be meaningfully given orders are those that are not yet engaged or are ranged units. In turn, these orders can be divided into those that were part of the battle plan and unplanned responses to a changing situation.
A planned order can be given very quickly, especially if flags are employed. If the commander on the left flank has been told "Advance and secure the bridge when a green flag is waved three times" then he'll have a couple of eagle-eyed subordinates watching the army command group for that flag and he will have tasked each of his centurions so they know exactly what they are to do when he in turn waves a flag or blows a trumpet or whatever. Elapsed time from the general telling someone to wave a green flag three times to the centurions shouting "Advance!" could be less than a minute, assuming line of sight exists. Or the commander may not be looking for a flag, he may be following contingency orders regarding when to conduct action X, for example, "once element Y reaches location Z, execute action X". See the final paragraph for why this is more likely than looking for flags.
An unplanned order is a different story. A runner would need to be sent to tell the commander on the flank that things have gone pear-shaped and he needs to send a couple of centurions with their troops over to the other side, or whatever. (Contrary to another answer, medieval archery did not have the accuracy or range to be a significant threat to a runner moving to the rear of units that had not engaged.) The possible variations in terms of who has to go where and do what are so great that it is infeasible to have pre-arranged flag signals for all of them. Which means that it will take time for the runner to reach the commander, then the commander will need to either summon or send runners to his centurions for a quick orders group (O group). Depending on the complexity of the orders, the centurions will each then either return to their troops and shout "Follow me!" or they will need to call their captains in for a quick O group. The exact time before soldiers start moving in response to the general's new requirement could vary from minutes to an hour or more, depending on the distances involved and the dispersion of the troops. (If you want to know how long it would take in a particular situation, roleplay and time the conversation that would occur at each level and add the necessary transit times for the runners and commanders.)
A few more things to note. First, medieval armies were small compared to both ancient armies and those of the Renaissance period. 25,000 soldiers is an enormous army for that period. (The French may have had 25,000 at Agincourt, if armed servants are counted.)
Second, armies were organised along feudal lines - Lord X would be told to bring along a number of troops and he would pass the requirement down to Baron Y who would in turn tell Sir Z. These troops would be made up of the nobles, a few trained retainers and mostly a bunch of peasants taking time out from farming for the summer. Each noble would command their subordinates and the overall level of training was very low. The lack of training matters here not because of fighting ability - the conscripted peasants on the other side were just as bad at fighting - but because they could not execute complicated orders well. Do not try to portray medieval soldiers as Roman legionaries or Greek phalanxes or Renaissance professional soldiers moving in neat squares as ordered, because this was amateur night in comparison.
Third, another consequence of the feudal organisation and amateur nature of this army is that there were generally (no pun intended) no "quarterback generals" - an army would be led by a noble who was expected to lead from somewhere near the front. Which means that the leader (albeit wearing much better armour than almost any of the other combatants) would be distracted by people trying to poke him with pointy things and would not be giving many orders at all after things kick off - subordinate commanders would be acting on their own initiative and/or contingency instructions.