Answer: Producing good healthy transplants at home is doable but not always easy. Timing of course is important, so are the growing conditions you can offer the plants. The most difficult to manage is usually providing adequate light, and after that the problem is usually one of not enough space to accommodate the plants as they grow.
First off, as soon as seeds germinate you should remove the plastic and put them in the brightest location you have. A south window may be adequate, but many gardeners prefer to use florescent light.
Seedlings need air circulation and must be thinned if they are crowded. Sow them as lightly as possible in the first place, and as soon as they are large enough to handle (two sets of leaves in this case being a rule of thumb as baby petunias are very small) transplant them to individual cells if you started them all in one container, or thin them to one per cell if you started several seeds per cell in six packs, for example. The reason you plant them individually is so they do not struggle for air, water, light or nutrients. Usually they are beginning to fill the six packs at transplant time, but since you started these so early there is a possibility you will need to transplant them to yet a larger pot before planting them outside.
Once they have germinated, most annual seedlings grow nicely at a temperature a bit cooler than the normal room, say 60 or 65 degrees. As they grow you will need to raise the light to keep it within a few inches of the tops of the plants. Eventually you can move them to a cold frame to harden off or gradually acclimate them to being outdoors over the course of a week or so. When the weather begins to settle, somewhere around your last average frost date you can plant them in the containers outside. Keep an eye on them and be prepared to cover them at night if a cold snap hits.
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