Place quart-size plant pots on a table or place them side by side inside a large tray to make transporting them easier.
Fill the pots with bagged potting soil until it rises to 1 inch below the upper rim of each pot. Smooth out the top of the soil and then poke two 4-inch-deep holes in the soil of each one. Space each hole 1 inch apart in the pots.
Open an envelope of seedless watermelon seeds and insert one seed into each hole. Add more soil to the top of each hole until filling them completely.
Water the pots until all of the soil mix is moist and it begins to drain from the bottom of the pots.
Place the pots in an indoor location that maintains a constant temperature of between 75 to 85 degrees Fahrenheit. If needed, place them on top of heating mats to maintain the proper temperature.
Monitor the pots daily for germination. Do not water the soil from the time of planting until you see the first sprout appear above the soil line.