That is a big question! I think the most important thing is to know how the apartment situation works here. It's different than most other cities (and definitely from New Hampshire). If you don't already know, it's very expensive (most young people here are paying more than the recommended 30% of your income). If you're looking for an apartment and hoping to find roommates, your best bet is actually with Craigslist. Do some research into neighborhoods first and your commute time so you don't end up in a great looking apartment that is two hours to your job.
If you're looking for an apartment with other people or on your own, there are apartments with and without broker fees. Personally, I try to avoid broker fees (particularly after an apartment fell through). Sometimes, it's unavoidable, especially if you're looking into luxury apartments.
+ http://www.trulia.com/real_estate/New_York-New_York/crime/ (don't let this dissuade you from all places, but it's good to be aware of what the neighborhood you're interested in is up to)
You may not be able to find an apartment more than two weeks out. It moves fast here, so don't let that dissuade you. And temporary sublets can be a great way to get you into the city without being stuck in the apartment forever.