>>55192652You pay 200BP for them to come once. If you beat them in battle once, they give you an item. You do not need to fight them again after beating them just once unless you want to grind money. They will leave by themselves after 6 hours of real world time. Only two coaches can be present at a time so yes you can invite a third one and it will push the first coach out, allowing you to call for them again without needing to wait any amount of time. When you invite them the second time, make sure to talk to them. If they're having a conversation with another character then still make sure you talk to them again afterwards. If you're unsure then keep talking until they ask you for a battle (unless you've already fought them on this invite in which case they'll just repeat the same two lines over again).
The third time someone is invited, they'll offer to trade Pokémon with you after speaking with them, provided you didn't skip talking to them on a previous visit. After trading, there will be a golden ring around their profile picture on the computer so you know that you are done with them. Unless you just want to rebattle them or have them interact with other characters, which doesn't have any reward other than the text attached to it.
Make sure to talk to the Blueberry Elite Four every day and battle them once as well as they'll also offer to trade with you, but for them you have to wait until an entire real world day has passed by before they'll refresh.
You unlock more coaches by completing trades. For most teachers you'll also need to have finished their quests at the academy in the base game, go to the academy and check if there's any ! besides a room if you're unsure.
That about covers it. I wouldn't normally spoonfeed this much but I was a little confused about how it worked too and Serebii and the like weren't clearing it up entirely.
