First, choose your outfit in the tutorial.
Three starter monsters will appear. Don't tap on any of them—instead, just walk around.
Continue walking for a bit and...
...Pikachu will appear!
Hit him with your Poké Ball to capture him!
That's it! He ran away from us four times (our throwing skills apparently need work), but even if you mess up, just be patient! He will definitely appear again!
While you'll have three other Pokémon huddled around you, as long as you don't tap them, you won't engage them. But this is also key—no matter how frustrated you get, don't tap randomly or you might end up losing your shot at that Pikachu!
Of course, you can find Pikachu in regular gameplay as well, but there's a certain satisfaction in having him in your Pokédex from the beginning.