Keep the seedlings moist, but water them carefully so you don't drown or disrupt them. Watering from the bottom works best, however a fine mist sprayer works well too. Once the plants have grown two full sets of leaves, transplant them to individual pots to give them more room to grow and develop roots. If your plants already have individual containers you won't need to transplant them. Handle plants carefully when transplanting, and grab them by the leaves, not by the stem.
Some plants benefit from being pinched back.
This helps them to be more bushy and colorful. This can also be used if your plants are getting too tall and you're not ready to plant them outdoors yet. When it's warm enough to plant outside, set the plants outside for a few hours a day for a week and increase the amount of time each day. This will get them used to being outside. When you're ready to transplant, water the plants and the ground where they'll be planted.