A major part of the Festival Plaza are the many Facilities you can build and use using Festival Coins. Facilities have different levels associated to them, denotated by stars starting at one-star and going up to five, depending on the facility type.
You unlock more Facilities by ranking up, and almost every rank, especially below Rank 20 or so, you will be introduced to new Facilities consistently from Sophocles.
Your Festival Plaza can accomodate a maximum of 7 Facilities at one time. To build a new Facility, you'll need to choose a Facility to get rid of. But if you're happy with your current Facilities or the Facility being introduced isn't that great, you can simply opt to not build it.
Note that certain Facilities and ranks are exclusive to certain versions, but can be purchased with FC from guests visiting your Plaza if you have enough, and other facilities and ranks are exclusive outright and simply cannot be obtained without having the proper game version.
By the way, you can speak to the construction guy on the right side of the castle and he'll help you rearrange your Facilities. The most notable use of this feature is that the first Facility in your list is the one that other players can buy from you when you appear in their Plaza.
As Luxurious as the Castle
Don't worry about the version exclusivity that has been cropping up in the Festival Plaza in droves. You can easily beat the main game and enjoy the meat of the postgame without ever touching the Festival Plaza aside from ranking up your plaza. Facilities are absolutely not needed to make the most of your experience!
As with Missions, there's quite a few different Facilities, but they all have different categories which will be broken down here:
Bouncy House: Your Pokemon get put on various obstacle courses that will give them EVs. Higher ranked Bouncy Houses will give you more EVs.
There are three variants. "Thump-Bump Park" gives Attack and Special Attack EVs and is exclusive to Moon. "Clink-Clunk Land" gives Defense and Special Defense EVs and is excluive to Sun. Finally, "Stomp-Stomp House" grows your HP and Speed.
Restaurant: Feed your Pokemon yummy meals. You can boost EVs, Happiness, and even grow a Pokemon's level by one here.
"Rare Kitchen" is packed full of meals to boost a Pokemon's level. "Friendship Cafe" stocks food to increase Happiness and is exclusive to Moon. "Friendship Parlor" does the same thing but for Sun. Finally, "Battle Table" will stock meals that boost EVs. Higher ranked Battle Table Facilities are Sun-exclusive.
Fortune Teller: This is an oddball Facility. For the price of 10 FC you will either be given a new phrase you can use as a greeting or various other answers, or you will be told to talk to a specific person or go to a specific facility, and your luck for the ideal outcome is increased.
There are six tents: "Kanto Tent", "Johto Tent", "Hoenn Tent", "Sinnoh Tent", "Unova Tent", and "Kalos Tent".
Store: Buy items from here for FC! All the items here can be bought in the main game for Poke dollars so this facility is somewhat redundant, given that your precious FC is best used elsewhere for good you cannot get in the main game.
"General Store" offers a bit of everything, "Ball Shop" stocks Poke balls of various kinds. "Battle Shop" will give you packs of the X stat items. "Soft Drink Parlor" lets you buy healing items like Lemonade and Soda Pop. "Pharmacy" specialize in healing items.
Haunted House: For 10 FC, you choose a Pokemon to go into the haunted house course. When they emerge, they will be holding an item, and if you're lucky, two.
Higher ranks correspond to higher chance of getting the top prizes. This is a notable facility for being one of the few outlets by which you can obtain Bottle Caps for Hyper Training.
Lottery: This is different from the Hau'oli Shopping Lottery, which you can get a higher chance of winning by having Pokemon from different trainers.
It is completley random, and at a higher rank will have a higher chance of getting you jackpot. The top rank lottery, "Treasure Hunt", is one of exceedingly few places you can find the sacred Gold Bottle Cap for Hyper Training!
Dye Shop: You can dye your white clothes different colors through these shops. Certain colors are exclusive outright to certain games, such as Beige clothes with Sun, but it is possible to dye your white clothes red or orange in Moon, for example.
Meet a guest sharing that facility and buy it from them for FC. You will pay for the dye job with FC or Berries.
All Facilities can be only used once per day! In Facilities where you can buy multiple items for sale, each item can only be bought once in the same day! Come back tomorrow.