Victory Station

The Victory Station is the successor to the Battle Spot and is where various battles will take place. This includes how to battle with many players online. This is accessed through the main menu and gives you two options when you get to the index: Battle Stadium and Live Competition

However, on the Victory Station page, the game compares a load of data from players you have interacted with or are nearby locally or online and brings up a poll to see which players of which game have done the most things. The things compared are:
Caught the most Pokémon
Evolved the most Pokémon
Hatched the most Eggs
Had the most Link Battles
Traded the most Pokémon
Traded the most League Cards
Cooked the most while camping
Visited the most camps
Played the most at camps
Caught the most Dynamax Pokémon
Cleared the most Rotom Rally courses
Helped out on the most Poké Jobs
Used turbo boost the most times
Changed clothes the most times
Found the most items
Whistled the most times

The Battle Stadium is the new name for what was once called Battle Spot and contains a variety of features

Casual Battle is the Friendly ladder on the Battle Stadium. It allows for you to play in Single or Double Battles with up to 6 Pokémon. Here, you can use Legendary and Mythical Pokémon that you wouldn't be able to use in Ranked Battles

Ranked Battles are the standard Ranked Battle options in Battle Stadium. These run in Single and Double Battles with rules that cycle through every season. For example, Season 1 blocks you using Legendary Pokémon and Gigantamax Pokémon.

Like the Battle Tower, you are placed into various tiers based upon your success or failures in battle and you typically only get paired with other players in the other tier. If you win the battle, you will work towards the next tier but if you lose the battle, your position in the tier decreases.

You will get rewards through Mystery Gift at the end of each season based on your placement.

Online Competition gives you three possible options. The first is to participate in an Online Competition. This includes ones that are officially running which have their own special rulesets

The other options allow you to deal with Friendly Competitions. You have two options: Create a competition using various rulesets and restrictions, that you can then share and have people play in or play in other people's friendly competitions. You can search for Friendly Competitions to participate in, either through a list or by entering a specific ID of the Friendly Competition.

Introduced in Generation 7, rental teams are a new way for players to share the team that they have created, however in Sword & Shield, you can now use that team in Ranked Battle and Online Competitions. You have 5 slots within which to save a Rental Team

To download a Rental Team, all you have to do is go to the Battle Stadium and go to Rental Teams, enter a code for a Rental Team and you can put it in one of the five slots. Alternatively, you can share your own teams and get a code to share it out. This makes it publicly online so anyone can use the team if they have the code

Introduced in Generation 7, you have the ability to download various rulesets from the servers. These include rulesets for the Ranked Battle system as well as any Online Competitions. These rules can then be used in all battles you participate in online or locally.

Live Competition is the option to select for competitions in real life. This can be done in a manner where you create your own competition which other people can then participate in, or you can participate in other competitions. This would include all Regional, International and World Championships

This mode also allows you to watch other battles happening in a competition by selecting a special match code for matches in the competition.

This mode also allows for you to play in LAN play. If you have a Nintendo Switch with a USB LAN Adapter, you can activate LAN mode by holding L, R and the Left Stick in the Live Competition menu.