Congrats on graduating!
Acting in NYC is a very competitive business. The ultra-professional level (auditioning for big movies, television, and Broadway) is near impossible to do without an agent getting you appointments in front of the casting people, and it's also difficult to get an agent in the first place. It doesn't sound like you're at that step yet, so you'll be best focusing on things like student and independent films, and off-off-Broadway theater.
Maleficent has it right, all the way. Auditions for films and plays are listed weekly in Backstage, which comes out on (I think) Wednesdays. You can also buy a subscription to the website which gives you all the same information.
You need to have an 8x10 black & white headshot with your resume on the back. Most of the projects listed in Backstage will ask you to mail a headshot and resume to a specific address, and if they like what they see, they will call you. Other auditions just give you a general date and time to show up (these are called "open call" auditions), and when you get there, they will ask for your headshot and resume.
Headshots can be expensive, anywhere from a few hundred bucks to a thousand, plus the costs of reproductions. I know a few low-cost headshot photographers; PM me for some recommendations. Low-cost, however, is still a few hundred dollars.
That's a start. But actually, the best thing I can do is recommend a few books that I've read and think are great for actors just starting out in NYC:
An Actor's Guide: Making It In New York City
How to Sell Yourself As an Actor: From New York to Los Angeles and Everywhere in Between
Best of luck!