Sure, let's look at the Hundred Years War. Let's look closer, let's say you're an Englishman fighting at Agincourt. Against all odds, your vastly outnumbered forces just won the day, yay for you. More importantly for your personal interests, you've got a prisoner of war, and you know that he's a rich and important guy who can afford to pay you a ransom because you recognized his heraldry, or more likely you didn't recognize it but you did notice that the guy you captured has expensive armor. Cool, you're going to be able to ransom him and make some money. If you're a common soldier, you're being paid piss all, so looting the defeated enemy and ransoming prisoners is a significant boost to your paycheck (one notable example from Agincourt, an archer named William Callowe is said to have ransomed a prisoner and received 100 pounds, about 4000 times his daily pay of six pence).

First problem: you have to be able to keep your prisoner long enough to ransom him. That's great if you're allowed to take prisoners, but if orders come down to execute all the prisoners, you just killed your meal ticket, or you didn't and you're going against orders and risking being hanged. Again, this was actually the case following the battle of Agincourt, including one unlucky group of prisoners who were locked in a farmhouse, which when the order came down to kill the prisoners was then set on fire. But let's say your prisoner is the simultaneously very lucky and very unlucky Flemish man at arms Ghillebert de Lannoy, who survived being on the losing side with only minor wounds to his head and knee, only to end up captured and stuck in the farmhouse when it was torched, only to survive the fire and escape, only to be captured by the English forces again. Well, luckily the orders have changed and you're allowed to keep him alive this time.

So what happens then? If you're William Callowe or some other soldier, you don't actually have much ability to house or deal with prisoners long term, instead you would sell them to a higher ranking person in your army, (in Lannoy's case that person would be Sir John Cornwall) for a lesser sum of money that's still more than you've probably ever seen in your life, like Callowe's hundred pounds. If you're already such a personage capable of negotiating directly, all the better. Lannoy was transported back to England and held captive until he was able to successfully inform Cornwall of his identity (and ability to pay for his release). He and Cornwall then negotiated the terms of Lannoy's release, including a sum of 1200 French gold ecus (a French coin of somewhat variable value, putting the sum around 22500 sous, or 1350 French livre) and a horse (the horse was valued at 100 ecus). Cornwall also gave Lannoy a sum of 20 English gold nobles (a little over 6 and a half pounds) so he could replace his armor, though Lannoy's account doesn't indicate if this was due to it being damaged or stolen. While this process of negotiation was nice and peaceful between Lannoy and Corwnwall, it's important to note that some captors would employ the use of torturers during negotiations in order to 'encourage' the prisoner to offer more.

These terms, however they were reached, were written into a proper legal contract, signed by both parties with an attorney present, sometimes with a third party contracted to act as something like a modern bail bondsman, providing the sum of the contract to the captor if the prisoner didn't pay and then having legal right to try and reclaim his money from the debtor. For ransom of common soldiers where lesser sums of money were involved, these were were usually seen as unnecessary and the prisoner's promise to pay considered good enough. Whatever the scenario, upon an agreement being reached, the prisoner would be allowed to return home to obtain the money he owes his captor, either from his own funds, borrowing whatever he may need, or petitioning his superiors to pay for sending him into a losing battle (this last one very rarely worked out). This is likely to be a process of at least weeks, if your prisoner has a short distance to travel and ready access to the money, more likely months, and in some cases years.