If you have a new emblem, they have adhesive.
On an emblem re-use, I suggest 3M adhesive, the one which will allow removal if you need to, in the future, is the double-sided foam tape. You use it on the back of the emblem, trimming it with something like a single-sided razor blade, an Xacto blade, or similar. Then pull-off the removable piece, and be careful about where you intend to place it.
3M Double Sided Tape Mounting Tape Heavy Duty,Foam Tape, 16.4FT Length, 0.98 Inch Width
$13 a roll on Amazon (above). This is what I would use.
You can also try tracing the shape of the emblem onto the double-sided foam tape, and cutting it out with a good pair of scissors, and then carefully applying it to the back of the emblem, before removing the other side of the tape to affix it to the part.
To remove emblems, assuming you want to re-use it, I use a piece of monofilament fishing line, 'sawing' it back and forth until the emblem is off. Using some sort of solvent like mineral spirits to remove any residual gum on the part on-which the emblem was mounted, as-well as the adhesive on the emblem.
There is another product, 3M super weatherstrip sealant, which comes in colors, and will stick very-well to a painted or plated surface, but it can be tricky to apply without having excess weatherstrip sealant ooze-out of from behind the emblem. It's earned the nickname, 'gorilla snot' for a good reason, it's gooey, and it's difficult to remove if you use too-much. Your local auto parts store will have it, <$7 for a tube 2 fluid ounces/59 ml.
An orange stick (ask your spouse/girlfriend) may help in removing excess weatherstrip sealant if you choose to go with that. Being wood, they won't scratch painted surfaces or plated surfaces.
