Passive skills increase your passive abilities like HP/MP, defence, attack, recovery etc. They do not need to be applied separately. To learn them, you need the corresponding combat level and gold. The basic skills have 4 levels: Beginner, low, intermediate and advanced. A low level is not a requirement for a more advanced level.
Active skills are combat skills. They require gold, a particular job level and CP. For every job level you receive 2 CP. To use combat skills, simply drag them into your quick slot and double click on them or use the quick slot hotkey.
Plus Skills are additional skills. They improve your combat skills or give them special abilities like an increased range. They require, as with combat skills, a particular job level, gold and CP. Every skill can have up to 4 additional skills, however only with 1 additional skill for every symbol.