There are three words that native speakers of English often confuse at first in their studies of Russian:

1. The first one of those is дома, which is an adverb that means “at home.” It never changes its endings.
2. The second is домой, which is an adverb that means “home” in the sense of “homeward/to home.” It never changes its endings.
3. The third is дом, which is a noun that means “house” or “building” and occurs in the singular and plural of all six cases.

Today we are focusing on домой in the meaning “home/to home/homeword.” Here is a subtlety. In English we can say “She is home right now” and “She is heading home now.” The former indicates location, and the latter indicates motion. In Russian you have to use дома in the former sense because it is a location phrase, and you have to use домой in the latter phrase since it indicates motion. Note also that as an adverb домой cannot be used with a preposition:

That last example is particular interesting. When you want to specify that you are going to someone's home, the word домой can be made more specific by adding a prepositional phrase using к followed by the dative case:

Actually in the previous three examples it's more natural to leave домой out, but it's perfectly grammatical to include it.