The Tiagra shifter is controlled by cables. When cables stretch, they need to be tightened. Shifting problems are almost always a result of slack in the cables. Shimano builds Tiagra shifters with this in mind by adding a small barrel adjuster to the derailleur body to take out the slack in the cable. You don't need tools to tighten a cable with a barrel adjuster; just use your fingers.
Place the bike in a bike stand. Turn the pedals with your left hand as you use your right hand on the right-hand shifter button to shift the bike into the smallest gear on the back.
Turn the pedals with your left hand. Push the shifter lever one click to shift the bike to the next biggest gear on the back. If the chain does not instantly jump to the next biggest gear, reach down and turn the barrel adjuster two clicks counterclockwise. The barrel adjuster is located on the back of the derailleur. It is a black serrated knob with a hole in it. The cable passes directly through the hole.
Turn the pedals. If the chain does not shift up or it chatters as it shifts up to the next gear, turn the barrel adjuster two or more clicks counterclockwise until the chain moves up to the next gear smoothly and without noise.
Turn the pedals with your left hand. Push the shifter lever one click. The chain should move up one gear. Give the lever another click to shift into the next biggest gear. Shift the bike through all the gears until you get to the biggest gear in back.
Turn the pedals by hand. Push the shifter button to bring the chain back down the gears one click at a time to the smallest gear.
Push the shifter lever one click to begin shifting the bike back up to the next gear as you turn the pedals by hand. Listen for chattering as you shift the bike up one gear at a time all the way to the biggest gear. If you hear any chattering, turn the barrel adjuster one click at a time counterclockwise until the bike shifts through the gears without chattering.