Probably the most convenient and best way to get on to Roosevelt Island is to take the '''Tramway''', crossing over the 300-yard stretch of the East River from 59th Street on Manhattan. Board the tram on Second Avenue at 59th Street. One way fare $2.00; MetroCards accepted. You can transfer free to/from the subway or buses, with a MetroCard.
The F train makes a single stop on the island before continuing on to destinations in Queens or Manhattan and Brooklyn (depending on which borough you took the train from).
The bridge from Queens to Roosevelt Island can be accessed at the intersection of 36th Avenue and Vernon Boulevard. On the other side, if you're on foot or bike, you can take a staircase, elevator, or escalator down to the ground level through a parking garage. The alternative is to run/bike down the corkscrew ramp but this is not suggested since there is from time to time a risk of being run over by a bus.
The Q102 bus runs from Astoria, Queens, over the 36th Avenue Bridge, and runs up and down Main Street, serving the 2 hospitals, at the extreme tips of the island. Alternating buses serve one hospital first, and then the other. The fare is $2.00, payable by Metrocard, with free transfers available to/from subways or other buses. The Red Bus charges 25 cents per ride and takes you to various point on the island, including the tram station, subway station, and library, with no free transfers offered.