Formal:
* Есть кто-нибудь дома? (Yest' kto-nibud' doma?) - This is the most literal translation and is appropriate for formal situations.
Informal:
* Кто-нибудь дома? (Kto-nibud' doma?) - This is a more casual and common way to ask.
* Дома кто-нибудь? (Doma kto-nibud'?) - This is another informal option, putting emphasis on the place being home.
Note: You can also use the phrase "Есть ли кто-нибудь дома?" (Yest' li kto-nibud' doma?) which is a bit more formal than "Есть кто-нибудь дома?"
Here's a breakdown of the parts:
* Есть (Yest') - means "is" or "there is"
* Кто-нибудь (Kto-nibud') - means "somebody" or "anyone"
* Дома (Doma) - means "at home"