I'm afraid I must disagree with several who say just ignore the pain and play for long sessions. My experience with mando (the resonant meat slicer) and considerable experience, albeit many years ago, in amateur athletics where callouses grow on every part of the body, provides the basis for my own (and obviously superior) opinion:

Long sessions of abusing tissue results in thick callouses, but they will not "stick" for long, as they'll usually begin to flake off in fairly short order. They can also continue to be painful because the callous itself transfers pressure to sensitive - and injured - tissue beneath it. By playing for a long time you're only killing tissue on the fingertips.

I would suggest short, but frequent sessions of playing. Some people can play until there's "mild pain" but for most it's more a matter of a "until tenderness." Starting with 5 or 10 minutes at a time, after a long delay, usually is sufficient. With nylon strings, and on a guitar, one might start with 15 or 20 minutes(?) depending on how "aggressively" one fingers.

Rest for at least a half-hour to an hour as soon as the fingers feel tender, and then play again briefly as soon as you can pick up the instrument without feeling undue "hurt," usually after a half hour to an hour. By "stressing" the tissue of your fingers mildly, you send the message that "something tougher" is needed, and by giving it even a half hour or so to rest, the tougher stuff will start to form.

I generally find that "practicing" 5 to 10 minutes, then 10 to 20 minutes, then another few periods of about 20 minutes, for about 6 to 8 sessions, which with an hour between can be fitted into a single day, will "toughen" the fingertips enough for a 4 or 5 hour session with my mandolin on the evening of the same day, and with no pain after the evening session.

Without the "warmups" I can manage deeeep and persistent pain for a few days after an hour or two of session play, and the session alone produces "dead feeling" finger tips that peel off the callouses about 3 days later. Then once the callouses start to break up, I've got lumpy tender fingers.

If I do the "gentle" buildup, within two or three days I can get as much toughening as needed to play without regard to, and without suffering from, any pain from fretting the strings.

Superglue, gorilla snot, model glue, alcohol, etc., are all "treatments for abused fingers" or "compensations for inadequate development." A couple of days of careful preparation should be sufficient to allow you to play without pain if you play for short but very frequent periods to build up the fingers and allow "toughened tissue" to grow instead of just killing the skin.

Of course that's just my own opinion; but it works for me and thus is obviously superior all those opinions offered by people who like pain and or enjoy seeing others suffer.

John