In Classic Traveller, the assumption was that characters would not change substantially during play, thus character advancement was a very slow process, and rather sketchy. Here are some rules to make character advancement a little nicer.
Learning by DoingIf a character used a skill during a game session to particularly good effect, then they should remember this at the end of the situation. They should receive an experience tick for that skill. Typically, only one skill will get the tic per situation, (player's choice if multiple skills were used).
If the character does not have the skill used, thanks to JOT, etc., they can be tutored by someone into an immediate zero level for that skill.
This requires a determination task on your part, and a tutor to show you "how to use that vacuum suit". Without instruction, once the immediate situation passes, the character loses the zero level. Regardless, if you used the skill successfully, then you can gain an experience tick for the skill. This does not apply to the Jack Of All Trades skill itself.
Learning Through PracticeA character can elect to be practicing a skill, desiring to improve it. The character's player has to back this up during role playing, by devoting time each game week to practice. At the end of a game month, a character can gain one experience tick, to assign to a skill that they're practicing. The character can continue this work if they pass a Determination task.
Learning Through StudyA character can elect to be studying a skill desiring to improve it. As with practice the character has to back this up during role playing. If they have an instructor to guide them, then they can take one tick per week. If they don't, then they can take one tick per game month for a studied skill if they passed a Determination task. A character may not apply practice or study to the Jack Of All Trades skill.
Making a skill improvement checkIf, at the end of a situation, the character has ticks equal to the point cost of improving any of their skills, they can elect to make an improvement check. An improvement check is of Formidable difficulty, and they can use their DM for one appropriate characteristic on the roll. (which is most appropriate depends on the skill they're trying to improve) The Character also gets to add the experience ticks they've accumulated above the target for the skill as a positive DM to the check for that skill.
(Ex: If a character wants to check for Brawling +1 from Brawing 2, and they have 13 tic's, they can apply a +3 for the extra tic's ) If you make a character check, then the character loses all their ticks and the skill increases in level by one. The character also gets one tick added to improving their Education stat.
If the roll fails the check, then the character loses half their ticks (round in their favor). Ex: if a character started with three, they ended up with two ticks) for that skill, and you get no increase.
Improving your StatsAll rolled characteristics except Social Standing and Luck can be improved by training, be it physical or mental. The bonus takes effect after months of this regimen, and you must account for the regimen during role play. This regimen essentially uses the time a character devotes to practice and study, though a character often can't do both at once (although some physical skills can be studied in conjunction with a physical regimen). If you skip the regimen for more than a month, you lose the benefit to your program. Your Social Standing can improve through role playing (Gaining a good or bad reputation, rising in economic status and political power)
Difficulty of the TaskTasks vary in difficulty: The basic throw applies only to a task of "average" difficulty: one in which a person who knows at least a little about what they're doing can succeed about half the time under pressure.
Task Difficulty ModifiersVery Easy +4, Simple +3, Average +0, Challenging -3, Difficult -5, Formidable -7 Stat / Skill DM's: When attempting a general task, any relevant skill the character has can apply. If reasonable, the character's skill level can get applied as a positive DM to a general task throw. If there is no skill relevant to the task at hand, then a characteristic might be used instead. Check Characteristic DM's from My master sheet(positive or negative). In some cases, apply both a skill DM and a characteristic DM. If it seems likely that a particular skill is rather required for the task, and you don't have the skill (like trying to pilot a nose-diving fighter jet), then you have to make a plain roll of 8+ at one or more levels of increased difficulty (which might make the roll impossible). You can also get assistance to receive a "one-time" zero level in a skill.(See "Learning by doing" in Skill Advancement.)
Special TasksThere might be some special, predefined tasks for use during the game. Right now, there's at least one: the Determination task. A Determination task is typically of average difficulty (but might be harder with sufficient distractions), and you can apply both your Endurance and your Intelligence DMs to the task.