The usual method of advancement in GURPS is the award of several points at the end of a session. Usually between 2 to 4. It is somewhat bland and depending on the campaign it unrealistically causes a character to zoom up in points in relation to came time. This stands in contrast to the realistic nature of many GURPS rules.
Runequest in contrast does things more naturally. When a character succeeds on using a skill they put a tic mark next to it. When they can spend a week of rest time they can make a roll to see if they learned from their experience. If they exceed their current skill level (higher skills makes this less likely) then they earn +5% to their skills. High intelligence can modify this roll favorably.
In addition to learning through experience, a character can pay to learn new skills and train existing one. However training only works to bring up a skill to 75% after which they can only uses experience to learn higher skill levels.
This system has a lot of flavor, and feels more realistic. Plus it directly relates to game time.
GURPS has a section starting at page 290 of the Character Core Book about Improvement through study. Basically it takes 200 hours of learning to earn one character point.
You can learn on the job at a rate of 4 hours of job work = 1 hour of learning. You can try to teach yourself if it makes sense. This works out to 2 hours of self-teaching to 1 hour of learning. You can goto a school. This works out to a 1 hour of school = 1 hour of learning. A full college courseload for a semester of 21 weeks will earn 5 points in 5 different skills.
You can pay for intensive instruction in which you get 2 hours of learning for every one hour of intensive instruction.
The cost for these options depends on the campaign setting. For a TL 3 fantasy setting I would say teaching is a comfortable job so hiring an instructor for intensive training would set you back about $6,000 per month. In the Majestic Wilderland that would be about 1,500d (sp) or 3 gold crowns. But at 8 hours a day for 28 days you get about 448 hours worth of learning or 2 character points. 1 point every two weeks.
GURPS allows recommends that you allow time spent adventuring to count for certain skills. And that it should be considered at least intensive training. For example two weeks through a jungle may easily net you a 1 point in Survival (Jungle)
As for learning through experience. I thing the following addition would work out nicely.
When you succeed on using a skill you put a tick mark next to the skill. When you have a week to rest and reflect on your experiences you roll 3d6.
If you roll a 3 or 4 you don't learn anything.
If you roll under your skill you learn 1d2 points in that skill.
If you roll equal to or over your skill you learn 1d3 points in that skill.
If you critically succeed by rolling a 17 or 18 then you learn 1d6 points in that skill.
If your skill is 17 or higher then a 17 always succeeds but you only get 1d3 skill points. An 18 still always gets you 1d6 skill points.
This is not per session. If you adventure, rest a week, adventure again and rest again in the same session you get to roll to twice for any skills you succeed in.
While adventuring characters can spend at least 2 hours on self taught learning in addition to whatever they are getting.
The effect of this is that it ties the awarding of experience more heavily to the passage of game time. Existing skills will tend to improve faster especially in situations where characters have to use many of them.