There are many ways to advance your character. The simplest and most fundamental way to do this is to attend events. Each event you attend gets you 3 CP to spend on buying more of the skills you already have unlocked. Writing a Post Event Letter (PEL) within the deadline (within two weeks after each event) will get you an additional 1 CP.
The next way to advance is through Training. Each character has 3 Training Points that can be used as BGS each event to unlock new skills. You can also train in-game with a Teacher to learn new skills. Teachers can help you learn base skills that are not in your header, as well as advanced skills. There are a large number of advanced skills in game that you can discover through in-game interactions. These skills are mostly open for anyone to learn, although there are prerequisites for some advanced skills.
Another way to advance is by training into advanced headers. Some headers are well known in game while others are hidden and need to be discovered. Advanced headers are generally composed of a small number of special skills that give a header a unique build. Advanced headers also contain skills that frequently cannot be trained into without having unlocked the header.
The last way to advance is to be social. There are many organizations in game that can offer trainers to members. Many organizations also have advanced headers that are only available to trusted members. Remember though that each organization, whether player run or NPC run, has its own agenda, ethical and moral standards. If you join an organization and don’t follow their code and rules, you might find yourself kicked out. But don’t worry, there are many groups with a wide variety of codes, so every character should be able to find a group where they fit in.