Learn Russian: Пока! Я дома.

Пока is an informal way to say goodbye, just like "Bye!" in English. You use it with friends, family, and people you address with the informal "you" (ты). До свидания is the standard, more formal "Goodbye."

Where is the verb "am" in Я дома?

In Russian, the present tense of the verb "to be" (am, is, are) is almost always skipped. So, instead of saying "I am at home," you just say Я дома, which literally translates to "I at home."

Why is the word дома used instead of just дом?

Дом is the noun meaning a physical "house" or "building." However, when you want to express the location of being at home, you use the special form дома. It acts like a single word meaning "at home."

Don't I need a preposition for "at" before дома?

No, you don't need one! Because the word дома already has the meaning of "at home" built directly into it, adding a location preposition like в (in) or на (at/on) would be incorrect.