Typically, while driving down the highway, driver 1 pulls in to a left or right position (when highway structure permits)behind the individual he wishes to challenge. Driver 1 then flashes his high beam headlights a number of times to officially challenge driver 2. Driver 2 would accept the challenge by turning on his flashers or hazard lights, or decline the race by applying his brakes, thus activating his vehicle's brake lights and indicating to driver 1 that they decline the challenge.
If the challenge is accepted, driver 1 pulls along side driver 2. A few moments are spent prepping for the race by getting at the proper speed, which is usually determined by driver 2. Driver 1 then holds up a number of fingers to indicate which horn blast the race will begin on (typically 3). Driver 2 would nod in agreement, and driver 1 would then honk his horn the agreed amount (here it's 3). Immediately on the third horn blast both participants mash the throttle and begin the race. The race is determined in a number of ways, though normally it ends when the lead car has held a stong lead of at least 5 car links ahead of his opponent for about 10 to 15 seconds, the lead car pulls ahead and out of view of his opponent, or the trailing car quits. In this race, the lead driver CAN quit and end the race, and such would NOT be considered a loss.
Obviously certain conditions must be observed during these battles. From traffic flow, to weather, to course and surroundings, all things must be considered. Speeds commonly get very high and dangerous, though most races are held honorably, with each driver knowing when to quit.
Historically, these races were popularized in Japan in the late 80's with the advent of the modern Japanese supercars such as the Toyota Supra or Nissan Skyline. They are currently very common around Tokyo's super highways such as the Wangan or the Shinanobashi, whose traffic flow late at night and construction make for excellent venue. This kind of racing is gaining popularity in America, specfically late at night on multilane country highways and interstates.
This kind of racing is the primary backdrop in the video game "Tokyo Xtreme Racer 3"