Every class has it's own skill tree. To unlock the best skills you will have to get a level (or as many levels is required to unlock the next skill) of all the skills below it in the tree. You will be able to continue levelling up skills but they may not necessarily be needed to unlock the next skill. Each class has it's own set of skill trees.

Skill Chart

Above is an example of what a skill tree looks like. If no level is stated, the below skills are only needed at lv1. Move numbers do not mean anything, they are just to differentiate each move. The first avaliable moves are the ones at the bottom of the chart.