TLDR:
I never saw the rationale behind "You can't level up because no one is here to train you" restriction. Apart from the fact that this is just a fantasy game and meant to be played for fun so we can escape reality and hang out with friends for a while, why would anyone want to make having fun and going on the adventure more difficult than what it is? Why add more restrictions and paperwork and side trips back to town to find a spell user who knows the same spell list you are trying to learn? During down time, it's assumed the PCs are practicing, reviewing, training, honing skills on their own. Spell users would be practicing spells or reading scrolls/spell books, fighters would be sparring/training. Just the mere fact that the PCs are out adventuring and learning from those experiences should be sufficient to explain how/why/when the PC levels up.
It's Long, Can Read:
The rules state that when a player meets x-# of XP, that PC goes up a level. The reason for going up in a level is because they have been gaining experience along the way. I get there are some things in the game the people want a rational explanation for. I am one of those people! I like a little bit (maybe MORE than a little bit) of reality in my fantasy world, I'm funny like that. So here's how we handle these things:
Spells:
- A spell caster has his list of spells and information from someone (teacher, mentor, book stolen from a library). It has spells listed from levels 1 - 10 or more. The caster is only able to figure out how to cast Spell 1 through practice, trial and error, stick-to-it-tiveness, because it is the simplest of the spells to cast. Eventually, the PC figures it out and is able to cast the spell. Through practice, casting the base level spell, and trying to work on casting the Level 2 spell, he will eventually learn the level 2 spell. The directions/instructions are there, he just needs to practice. Maybe he slowly starts to grasp the magical essence flows and can manipulate them into what looks like the level 2 spell, then he can further finesse those magical floes to sculpt them into what resembles a 3rd level spell.
- A fighter (or other non-spell user) wants to learn a spell list. It's extremely difficult and requires far more time and practice at the expense of his other skills (i.e.: fewer DP to spread around to the other skills.) Eventually, through hard work or just dumb luck, he succeeds at casting the spell. He gets the feel for manipulating magic energies but never quite grasps it fully and the really complex spells (level 6+) are just beyond his scope.
Fighters:
- Practice, practice, practice. Repetition. It is often said that to truly master a technique, it needs to be practiced 10000 times. A teacher/trainer doesn't change the fact that the PC needs to practice on his own, without the oversight of a higher-up.
- Real life experience. There is no substitute for experience. I don't care what you learn in classes, I don't care what you read from books, and even sparring in a class with fellow students does not prepare you for a real world fight where someone genuinely wants to hurt you. You learn a lot very quickly when your first real fight comes at you. Adventuring, fighting, killing orcs and goblins, getting beat up by a better fighter are all learning experiences that cannot be taught by a sword master or trainer. The PC learns these lessons and improves. You, the PC, whomever, picks up little moves or techniques from their opponent that they in turn try out for themselves and add to their skill set. "Hey, in that fight, I noticed he kept his left elbow lower to protect his flank. I usually slip a sword strike there but his elbow was in the way. I should try that."
* - I started Martial Arts in 1983 and I have quite a bit of experience. Quite some time later in life I was in a real fight and things were very different in a real fight. Training helped me tremendously, but it is very different having that practical experience.
Thieves:
- Someone (spy master, guild member, crooked uncle) teaches the PC how to pick a lock or to pick a pocket, but that only goes so far. It's still down to the PC to practice on their own (Tightrope walking, rope mastery, acrobatics, gymnastics, etc.). All the talk in the world won't improve the ability until the PC tries it and practices it over and over. Reading a book about picking a lock isn't going to help me pick a lock faster until I practice picking a lock. The PC would be practicing on their own, or learning something from "real world" experiences. "That style lock is pretty popular in this region. I found this lock pick with a slight bend at the tip seems to open the lock quicker. The lock maker must have tried to thwart would-be thieves by changing this design a little. I'll have to try that in the future, I bet I can pick similar locks faster."
- Practice, practice, practice. I can pick simple combination pad locks. I started on my own bike like back in high school because I noticed the lock was very loose and my mother must have bought me a crappy lock and chain to save money. I used to practice opening that lock at night, in the dark just for fun. I noticed my friend had the same lock I had so I picked his bike lock. He was surprised, thought it was cool, and wanted to know how i did it. At school, I noticed another friend had the same lock I had so I picked that one too, moved his bike, then locked it again. He thought it was less cool and was pretty pissed. The next day he had a Kryptonite lock. No one taught me, I just did it. I practiced, I observed, I practiced more. Pickpockets..... I never learned how to do that. I tried on friends and family, but I never ever got the hang of it. I was really interested in magic as a child and had the magic sets as-seen-on-TV, the works. In those books were the sleight of hand tricks, and reverse pickpocketing to plant the "card" on the audience member. I just never got the hang of it. Not enough practice or real world experience.
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This is just what we do in our group and it's worked for decades. I have die-hard players from that D20 gaming system and they often ask "Can we head back to town so I can find someone to train with so I can level up?" Or they find they have enough XP to level and up they don't. After a bit I notice they are still rolling the same stats and haven't leveled up yet and I ask why. "We haven't been back to town, so I didn't level up yet." But it's been 3 sessions since you leveled up! Why do you have to be in a town in order to learn from your experiences?