Twist the barrel adjuster on both the left and right shifters, between the shifter body and cable housing, clockwise until it stops, then turn the adjuster one turn counterclockwise. This will give you the ability to make minute adjustments to the cable tension later.
Locate the rear derailleur cable stop by following the cable from the right shifter to where it is secured to the derailleur at the rear of the bike. Loosen the rear derailleur cable stop using a 5 mm hex wrench. Use a pair of needle nose pliers to pull the cable taught underneath the cable stop, then re-tighten the cable stop.
Locate the front derailleur cable stop by following the cable from the left shifter to where it is secured to the front derailleur. Use a 5 mm hex wrench to loosen the front derailleur cable stop, then just as you did with the rear derailleur, pull the cable taught and re-tighten the front derailleur cable stop.
Take your bike for a short test ride. Shift through each of the gears on your bike and pay close attention to the accuracy and quickness of the shifting action. If at any point one of the shifters appears to shift slowly from a small gear to a larger gear, twist the barrel adjuster of that shifter counterclockwise to tighten the cable. If either shifter shifts slowly -- or not at all -- from a large gear to a smaller one, twist the barrel adjuster of that shifter clockwise to loosen the cable.
Continue riding and adjusting the barrel adjusters until your bike shifts flawlessly every time between every gear. Perform this procedure every few months to keep your bike running and shifting as smooth as possible.