This information is taken from various sources including state laws, state driver's handbooks, and bicycle safety advocacy sites.
A bicycle is a vehicle. Any person riding a bicycle has all of the same rights and responsibilities as a driver of any other vehicle.
In most states, bicycles are required to ride as far to the right of the roadway as is safely possible. There are however certain conditions which allow bicycles to use the main part of the roadway.
FOLLOWING A CYCLIST
As you approach a cyclist, slow down. Avoid the use of your horn. Cyclists can usually hear an approaching vehicle and loud noises can surprise the bicycle operator, causing an accident. Do not follow closely. Bicycles can stop and maneuver quickly. Be prepared for a cyclist to swerve to avoid a road hazard. Young cyclists are particularly likely to make surprising changes in direction.
PASSING A CYCLIST
When passing a cyclist, wait until its safe, allow adequate clearance (usually about three feet) and return to your lane when you can clearly see the cyclist in your rearview mirror. Do not use you horn. Do not attempt to share the lane with the cyclist. Reduce your speed, follow the bicycle and wait for a safe opportunity to pass. Aerodynamic effects from winds off large vehicles can cause a bicycle to be suddenly pulled toward the larger vehicle by two or three feet, depending on the relative speed between the two vehicles.
RIGHT AND LEFT TURNS
A bicycle is not restricted to the right side of the road. Cyclists are required to use the turn lanes. Merge safely with bicycle traffic when turning. Do not make right turns across the path of bicycle traffic. It is common for an experienced cyclist to reach speeds of 20-30 m.p.h. and be closer than you think.
Bicycles are required to ride on paved shoulders, where they exist, or as far right in the lane as possible only when the lane can be safely shared by a car and a bicycle, side by side. Even then, there are certain conditions that allow a bicyclist to "take the travel lane," such as:
The bicycle is overtaking and passing another vehicle proceeding in the same direction
The bicycle is preparing for a left hand turn.
There are unsafe conditions in the roadway, such as fixed or moving objects, parked or moving vehicles, pedestrians, animals, potholes, debris or glass.
The lane is narrow in width making it unsafe for a motor vehicle and a bicycle to share the lane side by side.
Bicyclists are not restricted to the right lane of traffic. When the bicyclist is changing lanes to make a left turn, they are to follow the same path any other vehicle would take traveling the same direction.
When turning left at an intersection, yield to oncoming bicyclists just as you would yield to oncoming motorists. (You'd be surprised how many people fail to do this)
DO NOT blast your horn when approaching bicyclists -you could startle them, causing an accident. (And we really HATE that)
Look for bicyclists before opening your car door. (I've been "doored" a few times)
Expect the unexpected from children. Children on bicycles are often unpredictable in their actions. A common accident type for young cyclists is mid-block rideouts - entering the roadway from a driveway, alley, or curb without slowing, stopping or looking for traffic.
Look both ways at intersections before turning. Bicycles may be found riding incorrectly facing traffic and create special hazards at intersections. (This is a really stupid thing for a cyclist to do, but there are still a fair numer of people who think they are supposed to ride their bike "facing traffic". Not only is it illegal, but it increases the odds of a motorist coming from a side road or driveway to not see them.)
Be alert to the causes of the most common motorist/bicycle collisions. A motorist turning left will overlook or misjudge the speed of the oncoming bicycle traffic. When turning right, the motorist should slow and merge with the bicycle traffic for a safe right hand turn. Motorists failing to yield the right-of-way at a stop sign to a bicyclist is the third most common cause of collisions. At intersections, right-of-way rules apply equally to bicycles and motor vehicles.
And please, please don't throw things from your car at the cyclists! Not only is it illegal but you really could kill someone that way no matter how "funny" you may think it is.
Above all else, just show cyclists the same respect you show to other vehicles on the road. Umm, on second thought, maybe try and show us a little more respect. (I've seen how some drivers treat each other.)