-( Story related, cannot be missed )-
Shortly after you've obtained Arsene and return to the castle for the second time, you'll be able to go through the negotiation tutorial. While negotiations are a bit challenging, if you match answers to the personalities of the Persona, you will have a better chance of acquiring them. The goal is to down all enemies on the field and then prompt for them to lend you their power.
Later on, some Confidant abilities will make this easier by either allowing you to have another chance to influence them or by entirely skipping the negotiation and acquire them (if they panic and try to beg).