For the New York hotels you can make reservations in several different ways. First if you already have chosen the hotel you may phone there directly and reserve the room you like. Or you may phone special reservation service number and reserve a room through it.
You may also use internet to reserve the room.. There are special free reservation sites. It may be official site of the hotel which you have already chosen or just site which may look for the room for you in different hotels.
After you have chosen the site you are to fill in the application form with some information about your stay in the hotel to check the availability of the room you need. This information may include check in date and check out date, the number of adults and children coming to the hotel. You can also be asked to fill in the table with the room price which is the most preferable for you.
Such site can also ask you about the room preferences like number of beds, smoking preferences and some others. After you have done all that you should click Check Availability.
If there some rooms matching your preferences are available they will be dispayed. You will be shown the list of rooms with the short description and price for each room. In front of the proposals you will see the sign Reserve. You are to choose the room you like and click Reserve. In such a way your reservation will be made.