if you don't know where to start, etc, perhaps wise to go with a broker. you will pay 1-2 months worth of rent upfront, as a commish.
on the other hand, if you can not afford to or don't want to pay a commission, just try craiglist. go to new york craigslist, narrow your search down to manhattan, then upper west side. then further narrow to apts by owner (you can also try "broker no-fee", but in that case the fee is built-into the rent).
as of sunday, 10:15 pm EST, on craigslist there are at least 100-120 postings for rent by owners in UWS that are less than 24 hours old.