The easiest way from Granville Street to Rogers Arena is the Expo Line SkyTrain from Granville Station to Stadium-Chinatown Station. The station has exits that lead down to street level beside the arena, so you step off the train and you are nearly there.
Granville Station to Stadium-Chinatown
Granville Station sits on Granville Street between Georgia and Dunsmuir Streets, with an entrance beside The Bay and another on Seymour Street. If you are anywhere along the central stretch of Granville, that is the closest place to board. Take an Expo Line train and get off at Stadium-Chinatown Station, which stands on Beatty Street at Dunsmuir Street.
Inside the station, follow the signs for the street level exit toward the arena. The other exits lead up toward Chinatown and the downtown streets, so it is worth taking a second to read the signs before you head out.
Burrard Station is another Expo Line stop downtown, on Burrard Street at Dunsmuir. If you happen to be at the Burrard end of town, the same eastbound train works from there too.
Walking it instead
Rogers Arena is on the east side of downtown, and the streets between Granville and the arena are flat, so walking is easy on a dry day. A map app gives the best live route and time from wherever you are standing on Granville Street. On event nights the sidewalks near the arena fill with fans, so leave extra time and expect slow going in the last couple of blocks.
Game nights, concerts and the ride home
Trains get crowded just before puck drop and again as soon as the final buzzer sounds. Arriving early or waiting out the first rush after the event makes the SkyTrain much more pleasant. TransLink posts service notices for large events and any changes to the schedule, so check the trip planner on the day.
Driving is the least convenient option for a downtown event. Check the arena website for parking options and event traffic notices. If you are going out for the evening, a taxi or rideshare drop off is simpler. Compare prices beforehand with the taxi fare estimator or the Uber calculator, and remember that rideshare prices can climb when a crowd lets out. The Vancouver taxi page covers local cab service.