Basically, for every skill, spell school, discipline, etc. there are two ways you can become more proficient. One is your general "skill level" (or spell level, discipline level, etc.). The other is your level of mastery or "rank". Your skill level is improved through continual training and repetition. Skill mastery is improved by specialized training from masters of that skill, spell school, discipline, etc. who can teach you very unique elements of a skill.
Finding masters and doing what is required to receive training is a quest. Sometimes the quest is very simple, other times the quest may be extremely difficult. Generally, the more advanced the training, the more arduous and sometimes dangerous the quest. A good start is to find NPCs you think might be knowledgeable in an area or ability, and then try asking them about the skill, spell school, spell sphere, discipline, etc. Sometimes just asking them about skill ranks or spell ranks might provide a clue. Of course, finding a master is sometimes much harder than this so always be thinking and observing!
The quest for skill mastery will be an ongoing task that you will engage in throughout your entire life on Threshold. You will proceed from being Proficient in a skill/school/sphere/discipline to becoming an Expert, a Master, and possibly even a Grand Master.