Combat is turn-based and on a grid. There are a bunch of different battlefields depending on where you are fighting. You and your opponent can have up to 6 generals who each contribute one of their pokemon to the battle. All pokemon on a team take their turns together instead of each pokemon having their own place in the turn order. On your turn your pokemon can move, activate the general's special ability for some kind of buff and attack. Each pokemon only has one move depending on the species but they can vary greatly in their range, area of effect, damage, etc. It's been a while since I played but I'm pretty sure battles over control of the map have a turn limit, so you have to beat the opponent within so many turns to take over their territory and if you're defending you can either beat them or run out the clock. Any general whose pokemon you beat fast enough you can then recruit after the battle.
Outside of combat it's a simple kingdom builder. You assign your generals to different tasks which they succeed in varying degrees depending on their stats. Different castles will have different collections of buildings for you to develop but every kingdom has areas where you can encounter wild pokemon to catch. Instead of EXP your general has a link percentage between them and their pokemon and the higher the percentage the stronger the pokemon gets. Each general has up to two favorite types which allow for a higher potential link and one favorite pokemon species which is the only one they can get 100%. NPC generals can also unlock legendary pokemon. Pokemon also have an energy level which goes down the more stuff they do, so it's recommended you spend a turn every so often feeding your pokemon so that their energy goes up and they can perform better.