The number of speeds, or gears, on a bicycle is calculated by multiplying the number of rear cogs by the number of front chain rings. A bicycle can have as many as 21 speeds, thanks to seven rear cogs and three front chain rings, but in order for these gears to work, it's imperative that each derailleur cable be properly adjusted. Each set of gears, front and rear, relies on a Shimano brand derailleur. This derailleur is responsible for moving the drive chain from one gear to another, but requires proper tension on its cable in order to work.
Shift the drive chain to the smallest rear cog and the largest front chain ring. This will place the chain the furthest from the inside of the bike.
Use a 5mm Allen wrench to loosen the derailleur cable anchor bolt. This bolt is located on the bottom of the derailleur, which is located just below the rear wheel axle.
Turn the derailleur barrel adjuster all the way into the body of the derailleur. Resembling a small barrel, the barrel adjuster is located where the cable enters the body of the derailleur.
Give the barrel adjuster two turns in the opposite, or counterclockwise, direction.
Pull the end of the cable taught with a pair of needle nose pliers, and once again, tighten the anchor bolt over the cable.
Shift the drive chain to the next gear over. If the chain responds sluggishly, turn the barrel adjuster counterclockwise, or until the chain shifts cleanly to the next gear.
Shift to the largest rear cog and smallest front chain ring. The chain will now be in the innermost gear combination.
Loosen the front derailleur cable anchor bolt, using the 5mm Allen wrench. The front anchor bolt is located just above the derailleur, which is located just above the front chain rings.
Turn the barrel adjuster all the way into the body of the shifter. For a typical Shimano 21 speed mountain bike, the front derailleur barrel adjuster will be located where the cable enters the body of the shifter.
Turn the barrel back out two turns. Using your needle nose pliers, pull the end of the cable taught, and tighten the derailleur cable anchor bolt over the cable.
Shift to the next chain ring over. If the chain doesn't shift, turn the barrel adjuster away from the body of the shifter, and shift a second time. Continue your adjustment until the chain shifts without hesitation to the chain ring.