I live in Ohio and have a 10 foot eucalyptus tree in my back yard and I would like to take a cutting from it to keep as a house plant, for I know it can not make it though the winter here. I need to know how to take the cutting and how to root it once I do. I would welcome any help. Thank you
Eucalyptus won't root from cuttings. But what you could try is cut the tree down to a stump, and plant the stump up in a large pot which you could keep in a cool but well-lit room indoors; keep at 5 to 10°C through the winter. The stump will sprout readily, in spring if not right away. You can repeat the cutting back every time it gets too large.
If this specimen is growing in the ground it will not be transplantable after having grown 10' high. You will have to try and overwinter it where it is, probably with heavy mulching, or even burial, as might be done with a hybrid tea rose in a severe climate.