Depends upon which ruleset is in use in game:
CT: You don't...
Your character can take a sabbatical to gain 1 skill level. You can use the Bk 4 Instruction rules to increase skills of other characters... or pay NPC's to use it on you.
Numerous house rules grew out of this lack, however...
MT: Very slowly... keep track of AT's, and when AT's + Int/5 = 3+, begin rolling each session until it goes up. Each skill is tracked separately.
TNE: Initiative and skills are two separeate experience pools. Spend points upon skills you wish to raise for skill XP. Initiative XP can only be used to raise initiative (and if your GM is really nice, and bends the rules, maybe for weapons specialization out of T2K2.2, and/or combat skills.)
T4: mumble_mumble_mumble. Check skills used. Earn XP. XP + check allows roll at exnd of session to advance. Erase checks after rolling... IIRC. (NOT checking).
T20: gain XP in play. When sufficient, gain level in appropriate class. Service class gains only allowed if "in that service" or by GM fiat.
GT: Experience in GUPRS is (almost) just more character points, save that points gained in play are halved when spent upon attribute gains.
T5: when a skill is used under stress, it gains a check. At birthday, if no life pursuit, best two check totals go up one level each. If a life pursuit, most checked life pursuit skill and mosty checked other skill gain a leel each.
Other Traveller: Well... since it's the wild nature of gamers to port settings to other systems... however that system defines it. Since the systems used vary widely (FUDGE, CORPS, EABA, StoryTeller, BRP, Hero, TFTFV, even AD&D....) so does the methodology.