There is so much to tell, so many beautiful and instructive stories... Here are some useful tips for those just arriving.
First of all, when you land, don't be afraid of anyone or anything. The airport is a very safe place. Look around, figure out how to get to the Greyhound station, and head calmly to the subway. It's better not to eat at the airport—the prices are sky-high.
The subway (it looks a bit creepy, but that's deceptive; for me, these underground tunnels became like home) from the airport goes through Brooklyn. There will be some rough stations, and guys with very stern faces might get on :) Don't be afraid of them; act very confident, keep a 'poker face,' and enjoy the view out the window. Some crazy people or just random guys might approach you—don't be shy to talk to them, don't be afraid, and don't show that you're here for the first time and overwhelmed. Speak calmly and confidently. Oh, I forgot to mention, if you plan to stay in NYC for a while, get a transit pass...
Greyhound will probably be the 'most dangerous' place for you :) because all sorts of types hang out there asking for money. Don't walk around quickly and looking confused, and don't dress 'fancy'—travel in casual clothes. If I remember correctly, when you exit the subway, you go straight from the platform into the Greyhound terminal; the ticket counters are on the right if you need to buy one. Oh, about clothes... The second time I traveled, I had a bag with notebooks for university :) It had a towel, a couple of pairs of underwear, socks, pants, and a t-shirt...
So, you leave the Greyhound station and need to find a place to sleep (you can actually wait out the night there if you're afraid to go out... though there's no need to be afraid). Go up a few streets and head right toward the center; you'll see hotels along the way, go to them. Don't go left—you'll end up at 12th Ave, and there are no hotels there :) If you arrived in the morning or afternoon, walk around, maybe go up to 59th St. to the park, have a snack there, and catch your breath. It's fresh and cool, just keep walking. Don't go to McDonald's or similar cafes. If you want, look for 'China Buffet King' or something similar around 5th Ave and 42nd to 47th St. (look for a big red crab sign in that area). They have a buffet for $12-14 where you can eat well and tasty.
Housing: buy newspapers, call around. Don't go to Brooklyn to the Russians, specifically Brighton Beach—there's nothing interesting there. Moreover, that area really annoys me, and in general, try to have as little to do with them as possible; they are mostly pigs and will scam their own people.
Work, well, what can I say... you just have to walk around and look. Try asking the pedicab drivers; there are many Russian guys in the Central Park area, they'll tell you everything. The work is generally profitable. I worked at http://www.meyersmoving.com/—the phone numbers are on the site, call and ask. The salary was $8, but tips were $50-100 daily, almost guaranteed.
The main thing is don't be afraid; no one will stab you, kill you, or take your money for no reason. Keep a confident face. I recommend walking in Lower Manhattan, below 12th St.—there are beautiful areas and parks. Definitely visit Union Square Park (14-16th St. & Park Ave-Broadway) in the evening. I got a piercing somewhere in Lower Manhattan—there are tons of salons, $15 per ear :) + don't be stingy with tips. By the way, among other things on the 'wall of fame' at this master's shop, there was a personally signed photo of Philipp Kirkorov with well-wishes :)
Getting around by taxi is expensive. I don't remember the exact amount, but drivers (especially the guys) get very offended and angry if they have to give change :)
Remember, in Manhattan, a 15% tip is the absolute standard!!!
We often ate at Columbus Circle—there are wonderful fountains there. You can 'pick up' (buy) food at a nearby store and eat while enjoying the view of the fountain and the metropolis around you.

