Nintendo Switch will have a separate smartphone app to handle voice chat in online games like Splatoon 2, we know that. But your next question might be about what you should do if you want to listen to the game and other players talking at the same time, with a single headset. No problem, just plug this weird little adapter into, er, everything (via NeoGAF).
The adapter comes bundled with the official Splatoon 2 headset from Hori. That's one wire into your Switch, one wire into your phone's headphone jack, and one wire into the headset itself. iPhone 7 owners get extra wire fun since this thing almost definitely isn't Lightning-compatible - go ahead and plug your Lightning-to-3.5mm-jack adapter in as well. Oh, and the cables themselves are only .5 meters (about three feet) long, so you'll have all this dangling off your head when playing handheld if you're standing.
Before you panic, there's no reason to believe the vaguely squid-shaped doohickeys will be required to participate in Nintendo Switch voice chat. It looks like all it does is mix together the voice chat and game audio for output through one device. If you don't mind listening to the game through your main speakers and to voice chat through earbuds or a headset plugged into your phone, you probably won't need it. Further upshot: the headset itself looks kinda cool, especially since your inkling will be able to wear a matching pair in-game.
Still, it would be a hell of a lot simpler if you could just plug your headset into the Switch itself, or your pricey (but headphone-jack bereft) Switch Pro Controller. The voice chat app from Nintendo better be pretty cool to justify all this trouble.