I will simp[ly copy the referenced article for this topic as it is quite straight forward. The article specifically addresses the white or butterfly ginger lily. Propagation is done for other ginger lilies in the same manner.
There are two ways to propagate ginger lilies:
To propagate from rhizomes is quite simple. After the ginger lily has died back in the winter or has essentially gone dormant, dig up and divide a rhizome as per the article section Dividing Rhizomes. I have not used a fungicide to treat the rhizome and they still, most of the time, have come up. I have lost a couple of rhizomes from rotting after having planted them so - probably a good idea to treat them. If you are going to save the rhizome for future planting or to give away - wash them off and let them thoroughly dry or they may rot. If you buy some ginger lilies from a dealer I would treat them. Generally, it is recommended to plant them just under the top of the soil - about 1 inch deep.
Seed propagation is a fairly 'quick' way to get a bunch of ginger lilies. Let the flower head dry on the stalk and if the flower has been pollinated, you can get the seeds from the dried out flower head. They may be red or black depending on the variety. Soak them for a couple of days and then plant them in a seed germination mixture you can buy from a nursery, etc. Put 1 or two seeds in a small pot/cup or seed tray you may have sitting around. I put the pots on a heating pad but this not really needed as long as you have an ambient temperature of 70-75 degrees. It will take a month or two for them to sprout. Patience is the keyword here.
Let them get a couple of inches of growth and then transplant to a potting soil mix in a larger pot and let them grow. They will not bloom in the first year as they are too small. I will not plant outdoors as there will be weeds coming up and if I planted the seeds 6-36 inches apart as per the article - guess which is a weed and which is a ginger lily?
I have a couple of dozen white ginger lilies growing that were seed propagated from last year and may bloom this year. Be aware the germination rate is not good - maybe 50% but it works.
That is it for propagation - continue to look around.
A white ginger rhizome looks like the ginger root that you buy in a grocery store. Use a flat-bladed shovel to dig up a rhizome. Take care to dig far enough away to avoid cutting the roots that grow from the sides. Wash away the soil with a garden hose and cut out anything that looks brown or rotten. Cut into 8-inch sections that have roots. Always make clean cuts; do not break the rhizome. Wearing rubber gloves, dissolve 1/4 cup of captan or other fungicide powder into 5 gallons of water. Drop your rhizome divisions into the solution and let them soak for at least 30 minutes and overnight if possible but not longer.
Planting Rhizome Divisions
Plant the rhizome divisions 1 to 3 inches deep in a rich organic soil. Plant the divisions horizontally and with a stub poking above the surface. As much as possible plant them same way they were growing before you divided them. If you plant rhizome divisions in the spring or summer, they will grow faster. Do not plant them in soggy soil or they may develop fungal rot.
White ginger blossoms eventually yield bright red seeds. Store seeds for three to four weeks at a temperature between 70 and 75 degrees Fahrenheit, and then soak them in warm water for two hours to soften their hard coats. Plant them 1/2 inch deep in compost. Keep the compost moist, in light and at a constant temperature between 68 and 77 degrees F. The seeds should germinate in two to six weeks but may take longer.
Plant seeds outdoors in a sunny location in soil mixed with humus, cover lightly and water generously. Plant the seeds 1 1/2 to 3 feet apart. Plant indoors in a soil-based potting mix. Do not plant outdoors if there is any chance the temperature will drop below 40 degrees F.