Know the language. Riders of tandems rely greatly on a team ethic. There are not simply two riders, but the captain and the stoker. The captain sits in the front seat and has control of the steering and most other navigational functions. The stoker sits behind and is responsible for pedaling and contributing to the forward motion of the bike.
Working together and remaining coordinated in every action is absolutely essential to an enjoyable tandem experience. Bill McReady, owner of New York's largest tandem shop, has a simple rule to guide tandem riders: "The stoker makes no mistakes." This means that the captain is responsible for any action taken by the bike. While the captain is automatically in charge of the steering and brakes, she is also in charge of putting down feet when at a stop sign and making sure proper traffic signals are used. This doesn't mean that the stoker can't be asked to give a clear traffic signal, but it does mean that the captain must delegate this responsibility in very specific terms. McReady's rule is simple shorthand to minimize confusion in situations where one rider may assume the other will do something.
One of the difficulties in using a tandem bike is the contraption's heaviness. The best way to start is to have both captain and stoker straddle the bike. Have the stroker sit first, lifting his legs until the bike is balanced entirely by the standing captain. Now for the teamwork. On the captain's mark the stroker begins pedaling, producing the necessary momentum to maintain balance. Then it is a simple matter of the captain lifting his legs finding the rotating pedals.
Riding a tandem is all about rhythm. Since the captain typically has control of the gear shifter, it is her responsibility to set the pace and speed. A good stoker will perfectly mirror the cadence and pedaling speed adopted by the captain. Like in a team sport, communication is essential. It is the captain's responsibility to announce when she plans to coast, take a rest or change gear.
As with any bicycle, both riders of a tandem should wear helmets. Additionally, the bike should have the proper lights, both a flashing white front light and a blinking red reflector on the back. Emergency stops can be very different experiences on a tandem. Don't be afraid to jam on the front brake, since tandems do not flip like a one person bike might. When braking it is best to use advance caution, expect your stops to take longer than on a normal bicycle.