Proficiency in a skillset is gleaned by learning from a tutor, or from another with a higher competency than you in that field. Professional skills are either primary (open to full mastery) or secondary (limited proficiency).
You are able to teach a skill to anybody else who satisfies the requirements of a basic knowledge of the skill, and being of a lower competency than you. Equally, you can learn a skill from anybody who has a higher knowledge than you do. It is not possible to teach skills to those who do not already possess it; they simply do not have the basic grounding necessary to begin to understand you. The only way to gain skills is to join guilds or perform specific quests where you may come into contact with 'brilliant' teachers who will be able to instruct you regardless of your profession.
Most guilds have two or three primary skills. These skills can be developed to the highest level without penalty since they are directly associated with their profession. Many guilds boast secondary skills which can only be learnt to lower levels. You will know when you have reached the limit of your progression in any skill by the fact that it is preceeded by "---->" in your SKILLS list. Specialist non-guild skills cannot be gained exception through extra ordinary circumstances such as divine intervention. See HELP ULTIMATE for information about the distinction between Ultimate (the highest skill rank) and crowned Ultimate (the highest possible point of progression in a skill).
Every character possesses a number of general and specialist abilities called skills. These skills determine your prowess and areas of expertise.