Once you're far along enough in the story, you'll be able to forge charms just like you can forge Armor and Weapons. Choose these if they're your most important skill, or a skill that requires a lot of levels to be most effective. Some armor, especially High Rank Armor, will have multiple levels of a skill on a single piece of armor.
For example, if you put on three pieces of armor that each have one level of an Armor Skill, that skill will now be at level 3. You can also see the Armor Skill page for a complete list of skills and all the armor that carries them. Then, you can see every piece of Armor (that you've unlocked so far!) that has a particular skill. After finding one you like, press R3 to sort armor by skills when at the forge.
This is the simplest way to increase your skill levels.