El policía va a ponerme una multa si estaciono cerca de la salida.

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Breakdown of El policía va a ponerme una multa si estaciono cerca de la salida.

• me: me
• a: to
• ir: to go

Questions & Answers about El policía va a ponerme una multa si estaciono cerca de la salida.

Why does it say va a ponerme instead of me va a poner?

Both are correct and mean the same thing: is going to give me (issue me) a ticket.

• El policía va a ponerme una multa (pronoun attached to the infinitive)
• El policía me va a poner una multa (pronoun before the conjugated verb)
  In everyday Latin American Spanish, both are very common; choice is mostly style/rhythm.

What grammar is va a poner? Is it the future tense?

It’s the ir a + infinitive construction (near future): va a poner = is going to issue/put.
It often corresponds to English going to and is extremely common in speech. The simple future (pondrá) is also possible but can sound more formal or more like a prediction.

What does poner una multa mean literally, and is it the normal way to say it?

Literally, poner is to put, but poner una multa is an idiomatic collocation meaning to give/issue a fine (a ticket).
Other common options:

• multar a alguien = to fine someone (verb form)
• ponerle una multa a alguien = to issue someone a ticket (uses le)