Learn Farsi: سنِ تو چند است؟

In Farsi, you don't literally ask "how old are you?". Instead, you ask "how much is your age?". The word چند means "how much" or "how many", and سن means "age". So the literal translation is "How much is your age?".

What connects سن and تو in pronunciation?

They are connected by the Ezafe, which is a short "e" sound. When you say سنِ تو (sen-e to), the Ezafe links the noun "age" to the pronoun "you", creating the meaning "your age" or "the age of you".

Is this exactly how Iranians ask for someone's age in everyday speech?

This sentence is perfectly correct, but in casual spoken Farsi, people usually ask چند سالته؟ (chand salete), meaning "how many are your years?". If they do use the exact words from this sentence, they will shorten the final word است to a quick "e" sound, making it sound like "sen-e to chande?".

How would I ask this same question politely to an older person or a stranger?

To be more polite and formal, you would replace the informal "you" (تو) with the formal "you" (شما). The sentence would become سنِ شما چند است؟.