Tie the slackline to the carabiner anchor at one end of the line with a Muenter hitch. To tie a Muenter hitch, make a loop near the end of the slackline. Clip the carabiner through the loop and around the long end of the line, and then tighten.
Tie the other end to the other anchor carabiner in the same way after tightening the slackline by hand. This approach is usually effective if the slackline is relatively short. For a longer slackline, you will need to tighten more firmly, or the line will touch the ground when a person's weight is applied to the middle of the line.
Set up a pulley system with two carabiners if you wish to tighten the slackline more tightly than you can by hand. Tie one carabiner to the line about 6 feet from the second anchor carabiner and then passing the line through the anchor carabiner, doubling back and passing it through the tied carabiner. For a greater pulley advantage, you can use more carabiners.