How to dry a eucalyptus plant and how to cut it back and will it come back next spring?
If it will come back in the spring depends on where you are, and what kind of eucalyptus you have. These are tropical plants, they don't generally take temps lower than 40F, although some will handle a few hours of below freezing. https://www.gardeningknowhow.com/ornamental/trees/eucalyptus/tips-growing-eucalyptus.htm
For drying, just cut the stems to a uniform length, tie one end of a piece of twine around the ends of the stems, then hang the bunch in a shady spot outdoors - a branch or porch - for a couple weeks.