That's the way to do it!
In England we have Punch and Judy Shows, which are performed on the beach for the delight of small children. That's the way to do it! is Punch's...er...punchline. The shows are extremely violent and ugly and most young children find them utterly hilarious.
Punch and Judy and all their friends are glove puppets:
Here's a close-up:
If you can't spot a glove puppet of any kind anywhere (which would be very sad) then there are always oven gloves, goalkeeper's gloves, thermal gloves...
A glove compartment is to be found in the dashboard on the passenger side of a car. It contains maps of places you haven't visited for months, half a tube of dusty sweets, and various letters that used to be urgent. Almost never gloves.
A glove box doesn't contain gloves either. It's a box with gloves sealed into the sides of it for handling toxic or radioactive substances.
If you're hand-in-glove, you and an associate are planning something closely; if you're handling someone with kid gloves then you're being very gentle and cautious. But if the gloves are off then you're being frank and merciless.
These are the sort of gloves that are off in that expression:
They're used, of course, to prevent serious injury when boxing...
...though not hitting each other at all would, I think, be even safer.
Spot the frippet: glove. This word comes from the Old English word glōfe, and is related to the Old Norse glōfi.
Oh, and by the way: bare-knuckle boxing was much less lethal than the wearing glove kind. It meant, you see, that it was the hands that got injured, rather than the head.