Starve the plants of water by ceasing irrigation to the problem area and the nearby surrounding soil. Club-mosses require water to live and reproduce, so removing that resource from the roots will stress and in some instances kill the plants, over time.
Don a pair of garden gloves, and rip out the plants with the roots and rhizomes intact, when possible. Grasp the entirety of the branches and foliage of the main clumps in your hand, at the soil line, and give it a good yank using your body weight to rip the plant form the soil. Return, and pull out all the smaller plant runners and all of the underground rhizomes that you can find. Bag all of the plant material, and remove it from the area to prevent rerooting and spore release.
Prune back overhead trees or shrubs to remove the shade or semishade that protects the plants from sun scorch and helps them retain moisture. Altering the preferred growing conditions dramatically in this way helps to keep the plants from spreading or reestablishing themselves.
Rake the now-cleared area to remove leaves, moss pieces, rhizome remnants, mulch and any litter, leaving a clear soil surface. Repeat this process every few weeks for the first few months to remove anything lying on the soil that can help create the moist, shady conditions that the club-moss requires.