Like many fruit trees, apricots rarely come true from seed. In other words, the tree that grows from your seed may bear little resemblance to the tree that it came from. Due to this problem, most fruit trees are grown by grafting stems onto rootstock. And if you expect the tree to produce fruit, you will need two seedlings since apricot trees require cross-pollination. Keep in mind this only improves the chances of getting fruit--there is no guarantee.
Cut open the ripe apricots carefully and take out the stones. Wash the stones to remove any excess pulp and then soak them in a jar of water for 24 hours. Taking the seeds from fruit that is very ripe will give you the best chance of success.
Remove the stones from the jar and wrap them individually in pieces of damp paper towel. Put the seeds in the plastic bag and seal it. Keep the bag in the refrigerator for four to six weeks to allow the seeds to break their dormancy.
Put a handful of gravel in each of your planting pots and then fill them with potting soil. The potting soil should be about an inch from the top of the pot. Take the seeds out of the paper towel and plant them in separate pots. The seed should be buried roughly half an inch below the surface of the soil. Place the pots in a warm, sunny location such as a window and keep watered just enough to moisten the soil.
Transplant your seedlings to the yard when they have sprouted. Spring is the best time to transplant them but be sure to wait until after the last frost. Choose a bright, sunny location with soil that drains well. Apricot trees do not grow well in very wet soil. Space the seedlings roughly 20 feet apart to allow room for the spread of the trees.