If you're trying to get to the North Shore, West Vancouver, or to Whistler, then simply follow the 99 highway from downtown. This road will take you over the Lion's Gate Bridge (one of the top 100 suspension bridges in the world), and will eventually turn into the Sea To Sky Highway which leads up to Whistler.
Best way into Vancouver coming from the States is Highway 99, once you get over the Oak Street Bridge, exit Marine Drive West and this will run you into Granville, straight over the Granville Island Bridge, into downtown! Otherwise take a left on 41st, where I think there is a turn signal (left) (rare in vancouver) and then make a right on Granville.
Advice for American Drivers in Canada: You'll notice three lanes while travelling around the main roads in either directions. Be wary of the right lane, many people park here, you'll be driving along and all of a sudden there's a parked car. Be careful. Also, be careful of the left lane, there are few left turn signals and many cars blocking the left lane waiting till its safe to turn left. Be careful. Also, you'll find some intersections you come to with only a traffic light for one direction. This is a pedestrian light area. Stretch your neck and try to view the opposite angled light, when red, it means you can go. Flashing green means pedestrians are crossing, be careful. Took awhile for me to learn these. Oh, Pedestrians have right of way, everywhere. and No U-turns permitted. Even if there is no sign.
The public transportation system is the worst nightmare in Vancouver. Most people travel by car since the buses take ages to come and the coverage of the skytrain network is very limited. If you are visting Vancouver, a rental car is an essential and it helps you save a lot of time.
If you plan on hitting the many natural spots of Vancouver (with the exception of the Queen's Park) you will need a truck.