Unless you are a blue Mage or samurai you normally can not self skill chain so you will need one other person to make one happen. They're made by you and someone else using the correct combo of weapon skills that result in said skill chain. Takes timing and practice. The skill chain can be then magic bursted by a mage who casts a spell that goes with the element(s) of the skill chain made on the monster targeted. Depending on the spell used it can cause a lot of damage or have the debuff not be resisted.