How to get apartment owners to respond to me on Craigslist NYC

The first trick is to respond only to legitimate ads.  There is a ton of spam and fraud on Craigslist.  The primary sign that an ad is not legitimate is that the apartment is under priced and/or comes with unbelievable extras such as 2 garage spaces. I took a look just now and found a bunch of large, beautiful looking apartments with off street parking that were impossibly under priced, look like apartments located in Chicago (not NYC), and that were listed in the middle of the night by people with ridiculous 3 part names.  I searched for keywords in the ad description of one and found the exact same text advertising apartments in LA and Philadelphia (How could a legitimate ad for a Lower East Side apartment claim it was "close to the bus line?" That's flyover country talk.).

But there are so many good looking deals, they can't all be spam or fraud, right? Sorry, the rental market in New York City is very efficient.  The probability that you can obtain a rental significantly below market is essentially zero.  A good place to learn what the market rate for apartments is (and what they will look like and what extras they might reasonably have) is the listings for no-fee apartments on Page on nybits.com. You will occasionally see mispricing there, although it is far more likely to be error than fraud.

Generally, legitimate by owner listings will provide a cellphone number, and you should use it to contact them. 

If you think it is a legitimate ad and you must reply by email, do so from a respectable sounding email address (e.g. not weedguy420) and do your best to convey that you are organized and are a qualified tenant: provide contact information, refer to the specific apartment you are interested in, indicate that you are employed and that your annual salary is more than 40 times monthly rent, state that you have good credit, and provide the lease start date you are looking for (If you don't have good credit and make over 40-45 times rent, then you have a different question: Why don't apartment owners respond to me if I have bad credit or insufficient income?).

If the ad you reply to is not legitimate, then at best you have given a spammer a live email address along with a modest amount of metadata about you (e.g. that you live in or are moving to NYC),  and at worst, you have engaged someone who will attempt to defraud you.  So to be clear, the 39 that didn't respond are likely to be spammers that will solicit you for services relevant to someone moving to or changing apartments in NYC and/or sell your email address to other spammers.  For this reason you might consider getting a temporary email address for your Craigslist apartment hunt.

And keep in mind the early bird catches the worm.  The rental market in NYC is always tight.  Keep track of the ad flow and respond to legitimate offerings when they are fresh, not after they have been out there for days.