Most likely by conventional means. There would also likely be NATO "peacekeepers" introduced into certain areas for specific tasks, but they'd otherwise seek to limit their engagement with Russia beyond that.
If it's a larger attack, or Russian forces go out of their way to defend to offending unit, things may widen from there because of that. But until the event happens, hard to predict as we don't know what the starting point is with respect to a "proportionate response." If we're talking "a few dozens/hundreds dead" cruise missile strikes are likely to be the extent of it.
Eh. I worry that a conventional response to a single tactical nuclear attack , which I believe would be the wisest choice because going nuclear is not necessary for victory by Ukraine, or necessary for NATO to achieve it's aims, would not be the response that Pooter needs in order to "escalate to deescalate". He wants to provoke a nuclear response on Russian soil to threaten strategic nuclear war to force NATO to pressure Ukraine to settle for losing Donbass and Crimea. So if he doesn't get the response he wants with a single attack, he may just continue throwing them over until he gets what he wants. This includes using tac nukes on any NATO peacekeeping forces that are sent in or possibly on NATO bases where conventional air attacks on Russia originated from. Simply responding conventionally and allowing Pooter to just throw tac nukes into Ukraine will eventually give Pooter the chance to win in Ukraine, which is looking more and more unlikely with each passing day.
To turn the tide of the war in Pooter would need to hit multiple targets in Ukraine with tactical nuclear weapons. Sumy. Nizhyzn. Chernihiv. Mena. Kulkykivka. Maybe Lviv. Vasyl'kiv. Ivano Frankivs'k. Myrhorod. Ozerne. Starokostiantyniv. Severodoetsk. Izium. Donesk. Logistics depots like Bila Tserkva, Dnipro.
Depending on what was hit, I don't see NATO just responding with "we'll take out that launcher". If the launcher was mobile it's probably on the road high tailing it back to Moscow. If it came from a plane you'd have to hit the entire air base it originated from. Probably within Russia.
While I personally believe that responding with a tactical nuclear weapon would be falling into Pooter's trap, I also see the catch-22 of not responding and Pooter feeling he can just continue to lob them over Ukraine until he can win. The simplest answer is just for NATO to enter the war full bore conventionally, without responding with nukes. But that just makes the NATO forces a new target for Russian tac nukes.
It may be possible to go head to head with Russia in an air campaign and missile campaign, targeting their nuclear delivery capabilities, without using nukes of our own, but it would be very risky and we could lose. All it takes is a few ballistic missiles getting through to NATO airbases and you're hurt. Air bursts near AWACs and electronic sentry aircraft would quickly blind NATO and take away much of it's advantage.
As much as I don't like it, I believe the best response would be to respond in kind with a tactical nuclear strike on a Russian air base or logistics depot. It would give Pooter the escalation he wants, but it would end the nuclear exchange there. Pooter would understand that NATO will go tit for tat with tac nukes, so he cannot win that way. He can only lose worse than he already is and take some of NATO with him. Pooter will threaten strategic nuclear attack. He will send his subs out. He will put his bombers on alert and have them circling like buzzards. He'll fuel missiles or open silo doors or put all the mobile launchers on the road or whatever. But I believe that it would be a bluff. This could lead to the Armageddon scenario, which I still believe that Pooter doesn't want because I honestly don't believe that he's that crazy. That he maintains some sense of self-preservation. That somewhere, he wants glory for Russia and turning Russia into glass isn't glorious. I believe that he understands that even opening the nuclear pandora's box very seriously increases his chance of getting lead poisoning. He's already paranoid in some ways.
This is my belief on the matter. It's imperfect, but I've given my reasoning behind it. I've heard doomsday scenarios and allegories but very little "this is the way it could actually happen" that make sense.
It's very possible that Pooter has NATO's number, though, and that a tac nuke attack on Ukraine would indeed cause NATO and world opinion to turn away from further assisting Ukraine. But it would probably cause a schism within NATO, and achieve the secondary aim of Pooter's War. And as usual, it does actually depend on where the United States ends up on the matter, because Eastern Europe, as much as it would like to, just can't go it alone. They need the NATO nuclear umbrella which is primarily an American nuclear umbrella, which they will be seriously in doubt of if NATO caves to a tac nuke strike.