One way to find information about bus stops along the Metropolitan Transit Authority's X1 route is by accessing MTA.info and looking for the bus schedules for Staten Island routes. Another website, Bustime.MTA.info, has a more complete list of the stops that X1 makes.
From MTA's home page, clicking on the New York City Bus drop-down menu in the Getting There section and selecting the Schedules link reveals a list of New York City boroughs. After clicking on the link to Staten Island bus routes, scroll down to the list of express routes, and click on the Hylan Boulevard link. This opens a PDF file of the bus schedule for the X1 and its main stops. On Bustime.MTA.info, entering "X1" into the page's search box directs you directly to a list of the route's stops.
From Staten Island, the X1 bus departs from Eltingville Transit Center on Arthur Kill Road. The bus then heads south on Richmond Avenue, making eight stops on this street as of 2015. Before reaching the street's end, the bus takes a left onto Hylan Boulevard. The X1 bus then leaves Staten Island via the Verrazano Narrows Bridge and crosses through Brooklyn without making a stop. It reaches Manhattan using the Brooklyn Battery Tunnel and makes several stops along the Avenue of the Americas before ending its route at Central Park.