How to fix the tension in these shifters?
Follow the cable from the shifter down to the front derailleur. At the derailleur the cable housing will end and the inner cable will continue to a screw on the derailleur that clamps the cable, take a moment to look at derailleur and find the lever that the screw is on and push it. That should move the cage of the derailleur (the part that shifts the chain).

If the derailleur is moving freely, check the cable it should be relatively tight and should move when you move the lever. If that's not happening – perhaps all you're doing is changing the amount of slack in the cable, then adjusting the tension should help.

The short explanation is to move the lever all the way up (to slack the cable as much as possible). Then loosen the clamp screw on the derailleur and pull the cable through to take up all the slack, then tighten the screw.

For more detail, check out this post on adjusting your front derailleur from Park Tools.