Fill a plant pot in the late winter with a mixture of equal parts of peat moss, potting soil, and vermiculite, and set aside a few ounces. Leave 3/4 inch of space at the top for watering and adding more soil. Dampen the peat moss before adding it to the mixture.
Sprinkle a few seeds on the surface of the damp mixture. Cover the seeds with another half inch of the mixture. Tamp the soil down lightly with the palm of your hand to make good contact between the soil and the seeds.
Water the planted seeds lightly until you see it dripping from the bottom of the pot.
Place the pot in a clear plastic bag and close it off to provide a humid environment for the seeds to germinate in.
Set the pot in a warm place where it will stay consistently around 70 degrees Fahrenheit for the next five to six weeks. Check the pot once a week to make sure the soil stays moist and to let in fresh air. Once the seeds sprout, remove the plastic bag.
Keep the anemones in a sunny spot where they will get at least six hours of sunlight per day. Water as needed to keep the soil damp but not soggy, allowing the excess to drain away.
Plant the anemone outside once all danger of frost has passed in a partially sunny spot where it will receive enough moisture without sitting in water. Amend the soil with some of the potting soil mixture if necessary to increase the amount of organic material and aeration of the soil.
Fertilize the plant in the beginning of summer with a few inches of well-rotted compost around the base of the plant to provide a fresh source of nutrients.