Generally speaking big papers like the New York Times are extremely difficult to get into. Your best bet is to start with regional and local papers. Here are some examples of op-eds that we had printed by following this approach. Note these are only examples by one author. These articles represent the newspaper's position on a given issue.
Any group of people can ask for a meeting with the editorial board.
It is best to have some sort of title for this. Look through back issues of the newspaper. If a person connected with the conflict comes through town, for example a human rights activist or a witness from Palestine, this is a good occasion to ask for a meeting with the editorial board. Most people are nervous the first time they go on the radio or on television. With practice it becomes easier and easier.