Getting to Gastown is easy: head for the waterfront. It's just east of Waterfront Station. Allow about an hour to explore Gastown—that's without shopping too much. Then, if you have time, continue on to Chinatown, where you could spend an hour just wandering around, checking out the architecture and exotic wares; add at least an hour if you also want to visit the Dr. Sun Yat-Sen Classical Chinese Garden.
Be aware that you might come across one or two seedy corners: it's all pretty safe by day, but you might prefer to cab it at night. The No. 19 Metrotown and No. 22 Knight buses travel east to Chinatown from stops along West Pender Street; the No. 3 Main and No. 8 Fraser serve Gastown and Chinatown from Cordova and Seymour near Waterfront Station. The Stadium SkyTrain station is a five-minute walk from Chinatown. From the station head down the Keefer Street steps, and turn left at Abbott Street. This will take you to Pender Street and the Millennium Gate.
Another option is to follow the Silk Road Walking Tour, a self-guided route marked with colorful banners. It starts at the Vancouver Public Library downtown and leads north and east to the main attractions in Chinatown, before the banners lead you back to the library.