Remove the plum fruit from around the pit. Wash the pit with cool water and scrub it gently with a soft brush to remove excess flesh. Set the pit on a clean paper towel to dry.
Fill a small bowl with water and let it come to room temperature.
Tap the pit gently with a hammer to crack the shell. Use caution so the seed kernel inside isn't damaged. Remove the seed kernel.
Place the seed kernel into the bowl of room temperature water. Let the seed soak for 24 hours.
Remove the seed from the bowl of water. Wrap the seed in a piece of paper towel and slide it into a plastic zipper bag. Close the bag and place it into a refrigerator for four to six weeks to cold stratify, which is necessary before germination will take place.
Take the plastic bag out of the refrigerator after 60 to 90 days of cold stratification. Remove the paper towel holding the plum seed and open it to reveal the seed.
Moisten a well-draining potting soil with water until it feels like a moist sponge. Fill a 4-inch-diameter pot that has bottom drainage holes with the moist potting soil. Plant the plum seed 2 inches deep.
Set the container in a warm area with a temperature of about 72 degrees Fahrenheit. Monitor the soil moisture and add water as needed to keep it evenly moist. Avoid letting the soil dy out completely or become saturated with water. Plum seeds produce a sprout after about six weeks.
Grow the plum seed until the seedling is about 6 inches tall. Gradually introduce the seedling to the outdoors by placing the container in a protected outdoor area for several hours. Increase the time the seedling is outdoors over seven to 10 days until you can keep it outside all the time.