There are many alstroemeria flower varieties, including the most popular, Alstroemeria aurantiaca, better known as Peruvian lilies. They have tuberous roots that are winter hardy in USDA zones 8 and warmer, as well as zones 6 and 7 with mulch. In colder climates, they must be dug up and stored in moist peat moss or vermiculite in a location that is about 40 degrees F. Wait to plant your alstroemeria flowers--either newly acquired or stored tuberous roots, or established plants--until the last frost of spring has passed.
Choose a site that is in full sun or has some light shade in the afternoon.
Turn over the soil 12 inches deep and mix in about 3 to 5 inches of compost, peat moss or another organic matter. In general, the more sandy or clay your soil is, the more organic matter you should add. For clay soils, mix in equal parts of coarse sand and organic matter to better improve water drainage.
Plant the tuberous roots so they are 10 inches deep and 10 inches apart from one another. Dig holes that can accommodate the roots and provide enough room to spread them out. Alstroemeria roots are brittle, so take care. If you are planting established flowers, plant them to the exact same depth as they are planted in their containers.
Water your newly planted alstroemeria with 1 inch of water and continue to water them throughout the growing season when it does not rain at least an inch per week.