Relocation to NYC from Australia - Standard costs of living?

I am 18 yrs old and intend to relocate to NYC from Melbourne, Australia in late October for an internship, but while having visited there numerous times as a tourist, the standard cost of living for actually residing there (for a minimum of three months) is completely beyond me! I was wondering if I good get some basic info in regards to rent for apartments, public transport, and other standard costs. Any insight into good places to look for decent rent and location would be much appreciated aswell! Thanks so much!