It takes two free slots to start a brand-new skill, but it only takes one free slot to improve an existing skill.
Melee weapons usually get a bonus if the character has high strength while missile weapons get a bonus when the character has high dexterity.
A character can role-play learning a new skill (under the GM's direction). For example, a character may spend six months in game time studying under a martial arts master learn Way of the Protective Hand.
Certain magical books will convey new combat skills.
A Player Character can cash in a wish to learn a combat skill.
Constructs can choose to either learn new combat skills or develop a new accessory.
Combat skills cannot be unlearned.
Certain character classes have limitations on weapon use. For instance, most forms of good-aligned Priests are limited to bludgeoning weapons.