Take care of the existing weeds. Cut long grasses or weeds as close to the ground as possible. You can spray them with an herbicide, but make sure to cover your plant with a bucket to reduce secondary damage.
Bring the material you chose to the area where you want to block out the weeds. Cut an X in the center, and place plants through the X. For larger plants, lay the weed cloth around the stems of the plants.
Cover the area around the perimeter of the plants with the weed-blocking materials as far out as you don't want weeds. Trim the excess with a pair of scissors, using rocks or other heavy objects to hold the material in place. Be sure to overlap the edges by a couple of inches to keep weeds from growing through.
Shovel 3 or 4 inches of mulch over the top of the weed barrier. This will hold down the weed-blocking material as well as make the area look much more aesthetically pleasing. Ensure the mulch does not touch the stems of plants in the center.