1) Most of the city is based on a grid system, divided into streets and avenues. If you start south and walk north you'll find 1st St., 2rd St., 3rd St., etc. East to west is 1st Avenue, 2nd Avenue, etc. We also have lettered avenues (A,B,C,D) that start east of 1st Ave.
2) Below Houston St. (The Village, Soho, Financial District, Little Italy, Chinatown, Lower East Side) is NOT based on a grid system and has name streets so...take a map.
3) Coming out of the subway can be disorienting so a) look for the next street to tell you whether you're going north or south or b) know that the traffic flow of the avenues alternate going uptown and downtown, so if you figure out one avenue (6th Ave. flows uptown) then you know you need to walk with the traffic flow to go uptown/north. From that you'll know that 7th Ave. traffic flows downtown, 8th Ave. uptown, etc.
4) Streets are distinguished by "east" and "west," as in "E. 16th St." or "W. 53rd St.," with the dividing line being 5th Ave. So E. 16th St. becomes W. 16th St., west of 5th Ave.
5) Also, starting from 5th Ave. are east/west addresses. 5th Ave. to 6th Ave. has "west" addresses 1-100. So 65 W. 58th St. would be between 5th and 6th Ave. Need to get to 325 W. 58th St.? Add 100 for every avenue so...it's between 8th and 9th Ave.
Again, these are things I've learned over time so don't worry if it doesn't all make sense right away. And last, one of my favorite pieces of advice: put away the map, wander around and get lost. Because sometimes the best experiences are the ones you find by accident.