Sales Tax Remittance Question 

I'm confused about sales tax remittance. That is, say I am in Utah, and I sell something to someone in New York, and I'm required to collect sales tax from the New York resident on behalf of the state (and city?) of New York then where do I send the money that I collected? It seems crazy that I might have to send a thousand checks to a thousand cities. It seems even more ridiculous that I would have to fill out paperwork for a thousand cities. How does this really work in practice?