There are ways of picking up skills that your character didn't start with. Any skill can be wished for, additional wishes for that skill will increase the dice put into it when you go up in level.
Some skills can be learnt in certain situations:
Backstabbing, Dodge, Find Weakness, Tactics, Two Weapon Combat:
These can be learnt by giving the Golden Gladius (won after 20 fights in the arena), to Bart, the Grizzled Gladiator
Bridge Building:
This is learnt either through taking Yrrigs, the Mad Carpenter to Jharod, the Healer, then talking with Yrrigs in Terinyo
- OR -
Killing Yrrigs when you find him, and taking his Manual of Bridge Building
Climbing, Detect Traps, Disarm Traps, Pick Locks, Pick Pockets, Stealth:
These can be learnt from the Yergius, the Master Thief in Lawenilithehl once you are a member of the guild, otherwise he just teaches you Pick Pockets
You can either train in the skills to get a direct boost, or you can train to have the die rolls increased for when you go up a level
Courage:
The Barbarian will teach you this if you kill 20 more of the first creature you killed
Healing:
Jharod, the Healer will teach you this if you show mercy by bringing Yrrigs to him
- OR -
The Kranf Niest, the Mad Doctor will teach you this if you kill Jharod for one of the quests Hotzenplotz, the Crime Lord gives you
Law:
If you complete both quests that Twyat Pare, the Sheriff gives you, he'll teach you Law
Literacy:
Can be learnt by eating literate corpses (like Dark Sages)
- OR -
Thundarr, the Dwarven Elder will give you a Potion of Literacy for killing a random monster
Smithing:
This is learnt from Glod, the Dwarven Smith
Swimming:
Give Blup, the Baby Water Dragon several Potions of Carrot Juice