Generally there are few ways:
Starting with a skill Edit
Look under classes and races to figure out what each race/class combo gets. All characters are granted Climbing, First aid, Haggling, and Listening. There are also special cases, like characters born under the star sign of Falcon getting Survival skill.
Learning in-game by guaranteed source Edit
|Bart||in exchange for Golden gladius||Backstabbing, Tactics, Two weapon combat|
|Blup||giving potions of carrot juice (one if blessed ; two together if uncursed)||Swimming|
|Yrrigs||talking to him after saving him (or reading Manual of bridge building)||Bridge building|
|Yergius||join thieves guild||Pick pockets, Detect traps, Disarm traps, Pick locks, Stealth|
|Guth'Alak||choosing "knowledge" as reward for killing black druid||Herbalism (or Gardening, if you already know Herbalism)|
|Jharod||if Yrrigs is saved and non-chaotic; alternatively by showing an 'act of mercy' (see Healing page)||Healing|
|Kranf Niest||as reward for killing Jharod (needs Save Yriggs quest)||Healing|
|Old Barbarian||after completing his quest and non-chaotic||Courage|
|Tywat Pare||if both his quests are completed||Law|
|Glod||5000 gold (depending on race and other factors)||Smithing|
|Thrundarr||getting potion of literacy through first dwarven quest||Literacy|
|n/a||Eating a dark sage corpse||Literacy|
Out of these, Yergius and Yrrigs will both act as trainers, increasing your skill in their specialty areas. If you give Yrrigs spare hatchets, he will train you. Yergius, on the other hand, offers both practical and theoretical training, in exchange for gold. Theoretical will increase the dice used for your skill, such that, for example, "+3d5" becomes "+4d5". Practical will train your skill, as if you had used it many times. The more practices that you pay for, the better the chance that your skill will increase during the next check.
Potions and Scrolls Edit
You can get a random skill via potion of education or scroll of education. Any skill can be learned this way. Make sure that the potion or scroll is blessed; otherwise, you might merely get a boost to a skill that's already known. Through Alchemy and Magical writing sets, you can create your own potions and scrolls.
All skills except for Alertness and Healing can be wished for. Instead of granting skills, wishing for "alertness" increases your Perception, and wishing for "healing" will grant full health. Starting with Alertness, then, grants your character a strategic advantage, since it's so difficult to acquire.
Bards get a random skillset at the start (with guaranteed skills, race skills and Music always present) and later on have a chance to learn extra skills as their class power.