Well, have you got a Poké Ball Plus? Right, well, you've basically already got everything you need to get a Mew.
You just need your Poké Ball Plus connected to your Switch to use as a controller - a simple process I'm sure you can figure out by yourself.
Once that's done, you can go to the Communicate option on the main menu, and select Mystery Gift. Receive your gift from your Poké Ball Plus, and Mew will be added to your Pokémon Box.
Taking your Pokémon for a walk
You can also place Pokémon from Let's Go onto your Poké Ball Plus to take them for a walk and earn them more experience.
To do this, simply go to the Save menu, and you'll find the "Take your Pokémon for a stroll" option. Then select either your partner, or a Pokémon from the Pokémon Box.
For obvious reasons you'll want to take good care of your Poké Ball Plus, especially if you've put a precious Pokémon onto it…
Getting walking experience
When you're out and about you can interact with the Pokémon in the ball to play with them. Kind of.
Basically hold the stick in for a second or two until you feel a vibration. From here you can shake the Poké Ball Plus in order to make it vibrate.
Shake it several times and the LED will glow and vibrate. I think that means the Pokémon liked it. Either way, racking up steps and playing with the Pokémon will reward it with experience when you bring it back to Let's Go.
Catching in Pokémon GO with Poké Ball Plus
When Pokémon GO is connected to the Poké Ball Plus, the ball will vibrate and glow green when you can either spin a Pokéstop, or catch a Pokémon.
To activate it you simply click the button on top of the Poké Ball Plus - not the button in the stick - and it'll spin gyms, stops, and catch Pokémon.
The only real issue with this is that the Poké Ball Plus will only throw out standard red and white Poké balls, and of course, you can't be using berries, so it's no good for grabbing Meltan candy either.