Various Personas can be acquired either by defeating Shadows during missions or through persona fusion. Personas you obtain can then be equipped on the protagonist character (Joker) by accessing the menu.
Characters other than the protagonist are only able to use their unique Personas in battle. This makes the protagonist the most versatile character of all since he will have access to a variety of abilities to take advantage of different enemy weaknesses.
Shadows that appear throughout various mission will occasionally drop a “mask.” Picking it up allows you to obtain the Persona from which a Shadow had taken its form.
You can also obtain Personas by fusing the ones you already have. Head to the Velvet Room to begin persona fusion. Note that fusing Personas requires you to pay a certain fee. Fusion services resulting in a strong Persona will usually cost more than those that result in weaker ones.