Like in most (if not all) games, you level up by gaining Experience Points (XP). There are 100 levels to each character and each time you level up you gain Skill Points used to activate new skills and level them up. It’s a bit weird how the skill points are given but here’s a little chart explaining it.

*You get 5 Skill Points every time you level up from Lv.2 up to Lv.69, except Lvs. that are multiples of 10 (100, 20, etc)

** Every Lv. multiple of 10 up to Lv.70.

After Lv.100, you won’t be gaining any more Lvs. but instead at a certain amount of XP gained you’ll be awarded with Skill Points so you can maximize their levels.