How can I reconnect the tension cable to the bottom of my overhead door?
There should be a cable on both sides of the door that go up to pulleys on a long rod mounted above the door. In the centre of the rod will be a large coil spring that is affixed at one end to the wall. 

As the door is brought down the rod rotates and winds up that spring. The spring acts as a counterweight for the door so it only takes a few pounds to lift the door rather than lifting the entire door weight.

When the door is fully open the spring should be relaxed. When open, each pulley can be untightened separately and turned by hand, or with a lever to adjust the tension on the wires.

DO NOT ATTEMPT that with the door down. There is a lot of energy stored in that spring.

Getting the tension the same on both sides is important to ensure the door travels true and mates with the floor evenly.