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Transplant the seedlings once they have two sets of true leaves. Use a large enough pot. Fill the pots with soil. Dig a small hole in the dirt. Transfer the seedling to the new pot. Pack the seedling in place.
"True leaves" refer to fully grown leaves, rather than leaves that are just beginning to grow. If you plan on keeping each pepper plant separate, a 2-inch or 4-inch (5-cm or 10-cm) pot should suffice. You can also combine multiple pepper plants into a single pot if it is larger. Use a loose, well-draining soil, preferably one with a high content of organic matter. The hole should be the same depth and width of the compartment your seedling currently sits in. If planting one seedling per pot, dig the hole in the center of the pot. If planting multiple seedlings in one pot, dig multiple holes that are at least 2 inches (5 cm) apart. Gently "wiggle" or pry it from the seedling tray by squeezing on the sides of the plastic compartment. Once the seedling has been removed, roots, soil, and all, place it in the hole. Pack the soil around the base of the seedling so that it is firm and steady.