You have a base competency with all the skills in the game. The only way to improve a skill is to succeed in using it. You won't succeed very often with low-level skills, but if you want to improve, the only way is to keep working on the skill until you finally start to get it right. Skills are rated from 0 to 100, but a 0 skill does not mean automatic failure, and a 100 skill does not mean you're guaranteed to always succeed. Furthermore, skill success can be modified by your applicable Stats, and sometimes be affected by external conditions beyond your control, in addition to your raw skill level.
For a complete list of skills, see below.
Some skills are used automatically in appropriate situations. For example, your weapon skill is checked every time you try to hit somebody with a weapon of a given type, and your Magic skill is checked whenever you try to cast a spell. Most spells, however, must be deliberately evoked from the skill list in your character window. You can also evoke some skills by using an item exclusively devoted to that skill, for example, using a pickaxe evokes the mining skill.