New York City is one of the most expensive cities in the world by pretty much any metric. That being said, there are still places where you can find a deal, provided you understand what you're going to get for your dollar.
You'll find New Yorkers talking about rent all the time. "How much are you paying for this?" is a common question that, for some reason, no one finds gauche in any way.
The main thing you should consider when looking for an apartment, assuming you're renting, is what does a home look like to you? Do you value being in a fun/trendy/up-and-coming neighborhood with a scene? Do you value personal space over shared amenities? Do you need to be close to a specific subway line because of your office location?
Generally speaking, unless money is no object, you can expect to sacrifice something you care about for something you care MORE about. As an example, a spot in a desirable neighborhood that is also in your price range is likely to be super tiny or shared with 6 other people. A big apartment (by New York standards, anyway) is likely to be in one of the outer boroughs or upper upper upper manhattan or in a neighborhood that is less desirable for safety reasons.
For reference, when I moved to New York City (in 2005) I moved with 4 other people and we shared a 4 bedroom apartment on the Upper West Side that cost $2500 a month. Split 5 ways that was a dream. It was a fourth floor walk up. Our neighborhood was in the process of being gentrified. I saw a naked man being chased down the main stairwell with a knife. But the rent! So cheap!
Three years later I moved further north in Manhattan, to another neighborhood that was being gentrified, into a 3 bedroom apartment split 3 ways for $2800. It had a washer and dryer in the unit. Still the best deal ever.
I now live with my wife. I've been in the city more than 10 years. We are in the process of finding a new apartment downtown. We are likely going to be spending $3500 or so each month for a space that's roughly 650 square feet. It'll be in a nice building, but Jesus. We are paying for it.
In short: it's all about finding what you want. There are a few websites that are great to put some of this stuff into context.
Streeteasy.com is incredibly useful as you can search for places without needing to consult a broker (you can search specifically for "no fee" apartments and save a lot of cash.
Nooklyn is also a cool site that specializes in Brooklyn-based apartments (on average less expensive than apartments in Manhattan, but not in all areas). Apartments are usually bigger there, and the site will also help pair you with a roommate in your price range.
Hope that helps. Good luck with the job search!
The city is what you make of it and you can always find ways to save cash. I lived with a roommate until I was 32. It's just something people do here. You get used to it.