The first of two DLC for Pokémon Sword and Shield starts with The Isle of Armor, which allows you to visit the new Isle of Armor region. Before you start the DLC, you will need to purchase the expansion pass from the Nintendo eShop. You can do so from the Nintendo Switch website, or directly from your Nintendo Switch. You will need your Nintendo profile synced to the website. The expansion pass will cost $29.99.
After you purchase the expansion pass, all you need to do is load into your Pokémon Sword or Shield game. You will receive a notification about how you have an Armor Pass, and you will be able to venture into the new region after you unlock The Wild Zone in your Pokémon game.
With your Armor Pass available and the Wild Area open, you can now travel to the rail staff at Wedgehurst Station. You can open up your map and travel to this region by clicking on it from your map and using a Flying Taxi to arrive at the front entrance.
Once there, walk inside and speak to the conductor in the green outfit after a brief cutscene with the new character who is being added to the DLC. For those who have Sword, it will be Klara, and those who have Shield will meet Avery. From there you can choose to visit the Isle of Armor, and you can now start your journey in the new region.