Step 1 · Pair Switch

In Pokémon GO: Poké Ball menu → Settings → Connected devices and Services → Nintendo Switch → Connect to Nintendo Switch → pick your game.

Then press the button above.

Step 2 · Send postcard

In Pokémon GO: Items → Postcard Book → pick a postcard → SEND TO NINTENDO SWITCH.

Then press the button above to receive it.

Requires a browser with Web Bluetooth support (e.g. Chrome or Edge on desktop or Android).