Using a skill makes the green bar progress. When the maximum is reached (no red colour left visible on the right), you need to train that skill with a teacher. A skill you can train is in yellow colour (instead of green).
To train, you'll need the right teacher, and spend Progression Points (PP, seen in your stats window), and Trias. The higher the skill, the more PP and money you'll need to be able to learn. When you have PP, you see a blue bar on the skills yellow bars; if the blue is shorter than the yellow, that means you don't have enough PP to train that skill yet.