Let’s begin by figuring out how to capture a monster. When you choose the appropriate option, you will be given a map of Spira and its 15 regions (that you can visit). In each area, you can set a Pod. Pods are used to capture monsters, mostly based on size: you will see Small (S), Medium (M), Large (L), and Special (SP). Creature size is critical in determining how your party works. You can have any combination of creatures so long as their "size value", adds up to three. Yuna, Rikku, Paine, and Small creatures are 1s, Mediums are 2s, and Larges are 3s. So, essentially, you can have three Smalls (1+1+1 = 3), one Small and a Medium (1+2 = 3), or a Large (3=3). (And, yes, YRP are included within this scope: you cannot have more than three things on your side on the battlefield.)
Special Pods are just that - Special. In essence, they can capture a number of types of enemies; pretty much any capturable enemy in the game. They’re only really useful for capturing Human species enemies; the others are readily delegated to other means.
If you need to know a creature’s size and/or loci - which is clearly important for this section, as we just mentioned it - you can see specifics in the following section, Creature Sizes and Locations. It is best to read up on the rest of this basic info, first, though!
You can only have eight Pods at a time, so it’s best to keep using them as you get them. They’ll be received from the storyline, releasing monsters, or winning within the Colosseum. Once you’ve gotten a Pod, select an area, then select the type of Pod to be used. The Pod will then be placed. Press R1 to try and get an enemy of that size type (or of something if Special). Sometimes, you won’t end up capturing anything, in which case you’ll see Shinra, indicating you can’t capture anything with that Pod in that area, and also indicating a Pod has been wasted. Otherwise, you’ll see the monster itself and get the option to keep it. (Either way, the Pod is lost, so it’s generally better to keep what you gain.)
The monster itself will NOT follow traditional enemy statistics guidelines. Most enemies you’ll find in the game, outside of Creature Create, have a definite stat level, like how the Assassin Bee always has 233 HP when not Oversouled. Like Yuna, Rikku, and Paine, they, too, can gain in levels and stats. They will start at a level determined by the girls’ level, although it’ll deviate from that by some number, typically 1-5 in our experience. You’ll generally want to try to get lower-leveled monsters, since you’ll need to level up most non-Humans five times to get their storyline complete. And higher levels means more EXP which is more of a pain.