Water the Gaura plant to a depth of 5 inches the day before dividing it. Run a hose on low volume at the base of the plant for 20 to 30 minutes to thoroughly saturate the soil.
Measure a 10- to 12-square-inch portion near the edge of the Gaura plant. Work the blade of a garden trowel around the edge of the portion at a depth of at least 5 inches.
Slide the blade of the garden trowel under the roots of the Gaura plant at an angle until it lays nearly horizontal. Work the blade around the bottom of the plant until the roots are free.
Lift the Gaura plant from the ground. Run water from a garden hose over the roots to wash away the soil and reveal the thick, fleshy rhizomes.
Locate a stem emerging from the rhizomes. Grasp the stem and gently untangle the roots from around the rhizome. Sever the rhizome using a pair of scissors or garden shears. Separate any large, well-developed rhizomes from the rootball.
Prepare a planting site for the Gaura rhizomes at least 3 feet from the mother plant. Loosen the soil to a depth of 4 inches. Prepare enough space in the bed to allow for at least 15 inches of space around each rhizome division.
Plant the Gaura divisions in the prepared soil by digging a hole large enough to accommodate the rhizome without bending it. Bury the rhizome with the base of the attached stem flush with the surface of the soil.
Water the Gaura rhizome to a depth of 4 inches immediately after planting it. Water it as you would the mother plant after the initial soaking.
Gather seed from a healthy, mature Gaura plant in early autumn once the flowers fade and are replaced by seed heads. Extract the tiny, papery seeds from the seed head. Store them in an airtight container until the following spring.
Prepare a bed for the Gaura seeds in spring when soil temperatures exceed 65 degrees Fahrenheit. Work the soil to a depth of 4 inches using a garden trowel. Break up the soil and remove any rocks or weeds.
Sow the Gaura seeds 1/4 inch deep and 10 to 15 inches apart. Sow two seeds in each hole to increase the likelihood of successful germination.
Water the Gaura seeds to a 3-inch depth immediately after sowing, then decrease water to 1-inch depth. Water the seeds only when the top 1/2 inch of soil dries out.
Watch for germination in 15 to 20 days. Thin the seedlings by removing the weaker of the two from each planting site. Keep the seedlings well watered for the first month, then care for them as you would the mother plant.