This is my first post here so if I'm doing anything wrong, please advise so I can correct it now and prevent it in the future.
Stories are rife with various methods of surrender, some more recurring than others. It makes me curious as to what would and would not work. First of all, I see several mentions--in fantasy books like ASOIAF, as well in a mid 19th century book I found--about knights (or, presumably, any soldier on such a battlefield) offering their gauntlet as a token of surrender. Is that accurate, and was it just any piece of armor, like "look, I'm removing my defenses, please don't kill me"? And while I know highborn warfighters and wealthy knights and such would be given more priority for ransom, but what's the likelihood some regular pikeman that was nobody before he was impressed into service could shout "I yield" and actually be spared?
First of all the standard disclaimer of "medieval" being a term of vast scope and fuzzy definitions. It encompasses a long period of time that saw rapid development and changes in society, it also includes several different cultures who may or may not have had different customs. If you specify a more narrow time fram and location you will probably get much more detailed answers.
Knights and surrendering.
That said, surrendering, in very general terms, would usually mean simply mean putting down your weapons in one way or another. Failing that, some other clear gesture that signifies your are done fighting would probably work as well, whatever you think your opponent would clearly understand as a surrender. Either because you are unable to continue the fight or because you make a choice not to. However, how attractive a prospect surrendering was depends very much on where and who you are. If you are a "medieval" knight, surrendering is not that horrible a prospect. You are reasonably likely to be treated fairly well and eventually ransomed. A rather famous example is Bertrand du Guesclin who surrendered at the Battle of Auray after Charles de Blois had been killed. He put up a valiant token resistance, then broke his sword to signify his surrender. He was eventually ransomed by Charles V for a tidy sum of 100.000 francs. Now, du Guesclin is of course an extreme example but in very broad terms still a good illustration of surrender on the battlefield for a knight. Even during the most vicious parts of wars, knights were geneally spared because they were simply more valuable alive.
Commoners, captivity and crusades.
What about if you're not a knight though? Again, it depends on where you are and who you are. In very very broad terms, surrender as a commoner is a much less appealing prospect. Odds are you will either be killed or enslaved. The English killed the French prisoners at Agincourt for example, partly in retaliation for the French attack on the baggage train/camp which killed a lot of civilians, partly because the situation was still unfolding and they were worried the French might break through and free the prisoners. If you're not killed it is more than likely you will be enslaved. Still slavery with all its horrors is still generally preferable to death. Still, given these two options most commoners would probably have prefered flight to surrender if they had a chance.
Muslim and Christian alike engaged in ransoming of valuable captives. Non-valuable captives were generally killed or enslaved depending on the situation, in other situations such as the Cathar crusade or the Northern crusade your prospect might be significantly darker. Forced conversion in the best case, extermination of captives and civilians alike on the other end of that narrow spectrum.
EDIT: If possible I would like to summon /u/Rittermeister to this thread who can probably provide more nuance if you specify a time and place.
EDIT 2: I also urge you to check out the posts by /u/TheGreenReaper7 here and here.