Used to ask about a countable number of things. Can also be used in statements meaning 'several' or 'a few' when not in a question.
How many apples are there?
I have a few questions.
Used to ask someone's age, often in a slightly indirect or polite way. Common with children or when age is uncertain.
How old is your child?
No matter how old he gets, he's still energetic.
How many apples are there on the table?
Excuse me, but how old is your child?
Happy birthday! How old have you turned?
幾つ asks 'how many' using the same native counting series as 一つ, so beginners sometimes confuse the question word with the number itself.