If you're wondering where you need to go to catch yourself the Galarian Slowpoke then our guide features exactly what you need to know to obtain it! This new Pokemon has been added in a new update to the game that was released on January 8th, 2020. This coincided with a bunch of big announcements at the Pokemon Direct.
You might have just put away your Pokemon Sword & Shield games, but be ready to pick them up in the near future! There's going to be two new expansions for these games that will include new Pokemon, and introduce the ability to catch some of the Pokemon that weren't originally included.

How to Get Galarian Slowpoke

You do NOT need to own the new expansion to get this Pokemon!
If you want to catch yourself a Galarian Slowpoke, you will need to make sure to update your game. When you load up your Nintendo Switch, you should immediately be prompted to update the game. If not, go to the home screen and press the + button on our Pokemon Sword or Shield game. Look for the "Software Update" option and see if there's an available update. Hit that option and your game should update to the most recent patch (1.1.0)!
Now that we have that updated, we're going to need to go into the game and travel to Wedgehurst! Once you arrive there, go south a bit and head into the train station that is very close to the fast travel point. A new kind of cut-scene will start, so wait for that to play. You will notice a new character in the area talking to one of the train employees. Talk to them, and another cut-scene will play. As this is going, a Galarian Slowpoke will meander its way into the scene! You will then be able to save your game prior to interacting with it if you want to soft reset and try for a shiny (I'm not positive this works).
Interact with the Slowpoke and you will go into a battle. It starts at level 12, so you can probably just throw a Quick Ball at it for the catch!
Watch this process in action with this video:


Evolving Galarian Slowpoke

You CANNOT evolve Galarian Slowpoke right now! You will need an item that can be found on The Isle of Armor which is one of the expansions you will be able to purchase:
Galarian Slowpoke can evolve into Galarian Slowbro if you use an item that can be found on The Isle of Armor. It can also evolve into Galarian Slowking if you use an item that can be found in The Crown Tundra.
Source
The Isle of Armor expansion will be release in March 2020! We'll update this guide with additional information once it has been revealed.