I'd love to visit New York but I'd be far too scared to work in any country where it's illegal.
Do people go to prison over there for it of is it usually just cautions/fines?
Also what's Hulu?
Hulu is a website that shows television shows, a bit like Netflix only it has a lot of currently running shows. You have to subscribe to see most content and that's impossible to do without a US billing address.
I can't answer your question about what happens to prostitutes with any real authority, but I can tell you that:
Every state is different in how they prosecute different crimes. That is, something legal in one state can be illegal in another and then you have different sentences as well as varying amounts of interest by local law enforcement. So, the situation will be different in NYC, LA, Chicago, etc.
That said, it is unlikely that anyone would get a prison sentence for one act of prostitution. I've never heard of it, at any rate. What is entirely likely is you will be held overnight until you can go before a judge. If you are arrested on a Friday night, you may sit in the pokey all weekend and then be taken in front of the judge on Monday morning, wearing whatever you had on when you were arrested. This appearance may result in being dismissed (unlikely), or your pleading guilty and being ordered to pay a fine as you leave, or perhaps given a court date with a bail set (if you don't plead guilty.) It is possible you will be held without bail until trial but that would be someone charged with a serious violent crime so extremely unlikely to happen to a prostitute.
Edited to add: what Amy said sounds true to me. You are unlikely to get arrested. I was just answering your question about what might happen if you are arrested.