Place the seeds in a bowl of warm water overnight or nick their hard coating with a sharp knife.
Sow two or three seeds in each of your peat pots, and cover the seeds with only a thin layer of potting soil to barely conceal them.
Moisten the soil with a watering can, and water them again whenever the soil dries out during the next four to six weeks.
Set the pots in a partially sunny area for a few hours each day after they sprout, and continue doing so during the next four to six weeks to help them acclimate to the outdoors.
Thin the growth in each peat pot by removing all but the sturdiest, liveliest vine.
Install an upright trellis or insert stakes in the ground approximately 1 foot apart in a sunny location. Moonflowers climb about 6 to 15 feet high and also sprawl out to the sides as they grow.
Dig a hole the size of your peat pot in front of each stake, and set each pot in the ground. After firming the ground's soil around the edges of the pots, water the area thoroughly.