Instead of asking "whose", in russian one has to choose between чей?/чьё?/чья?/чьи?
The choice depends on the gender of what you've found :) If you found something masculine, like телефон (ends in a consonant, so it's masculine. Also some masculine things end in -ь), then you'll ask: "Чей телефон?", "Чей словарь?", "Чей он?"
Neuter (ending in -o,-е): "Чьё зеркало?", "Чьё оно?"
Feminine (ending in -a,-я, sometimes -ь): "Чья книга?", "Чья дочь?" or "Чья она?" "Whose is the daughter, you're telling me about?"
Plural (usually ending in -и, -ы, sometimes -а, -я): Чьи книги? Чьи слова? Чьи машины?
Кого / У кого for beginners is usually about the live object (кого?) or the owner (у кого?):
Live object: Кого ты видишь? Whom do you see? <- we ask this if we assume the person sees a live object, not a thing. Кого is the version of "кто" in accusative case. We don't ask "кто" here, since "кто" can be only a subject of the question, not the object.
- Кто видит? Who sees?
- Таня. Таня видит. Tanya sees (Tanya is the performer of the action, so she's a subject).
- Кого ты видишь? Whom do you see?
- Я вижу Таню. (I see Tanya. Tanya is the object. I (subject) see (action) Tanya (my object))
- Кого ты читаешь? Whom do you read?
- Я читаю Чарльза Диккенса. I'm reading Charles Dickens (Чарльз Диккенс)
The owner: У меня есть телефон. У Тани есть телефон.
Instead of saying "I posess a phone", we often say, literally: "By ME exists a phone".
So the question will by just the same way "strange": By WHOM is the phone? У кого есть телефон?
Thanks God here you don't have to think about the gender:) У кого есть машина? У кого есть книги? У кого есть книга?
Answer: У меня! (By me) У меня есть книги, машина, etc.(By me there are books, a car etc)