1. Ideal Temperatures
When you are growing your seedlings you need to keep each seedling at its ideal growing temperature. Every plant's ideal temperature is different, most herbs prefer lower temperatures, while peppers must be above 60 degrees for best results. You need to do research on the seeds you are starting to make sure each individual plant is growing at the most desirable temps for the best results.
People will say "well I had my pepper plants out and it was 40 degrees and they look fine". Absolutely, they may look fine, but you likely also stunted the plants growth and when you put it out in your garden it will produce less even though there is no visible damage. On the other end of the spectrum, if your cold-loving seedlings get too hot they will bolt (go to seed) before you are even able to get them in your garden.
If you want your seedlings to be as strong as possible they need light. Lots of people start their seedlings in front of a window that gets only a few hours of light a day, I have done it myself many a times. The problem with this is your plants are going to reach for that light because they are not getting enough sun and will begin to get leggy. Leggy means the plants just have long skinny stalks. Eventually those seedlings are just going to fall over because their stalks aren't strong enough because they do not have adequate light. They likely will not survive outside either because they just aren't strong enough. This can also happen if you are growing in a greenhouse in an area of the world that is not very sunny.
If you want your seedlings to have strong stalks and be able to handle the wind once they are put in the garden they will need some artificial movement if they are being grown inside or in a greenhouse. You will want to start said movement as soon as they germinate. Start by running your hands over them very gently (like you were petting a cat) so their stalks bend back and forth. This movement will begin the strengthening process. Once they are a bit larger they need even more movement. A fan is a great way to simulate the wind. If you are growing your plants in a room with windows or a greenhouse with windows, open those babies up. This airflow also strengthens the stalks of your plants so they will be nice and strong when you plant them out.
Just like temperature every seedling is going to require a different amount of water to thrive. Some seedlings are going to be wet constantly, whole others want the smallest amount of water possible to keep them alive and any amount of overwatering will just destroy them. Once again, RESEARCH. Every plant is different and has different needs, the seed packet will not always give you this information, you will have to do your own research.
Stressing out your plants with the wrong amount of water will not always kill them but it will hinder their growth because they will be focusing on staying alive and not growing strong roots and leaves.
I killed a whole tray of pepper seedlings because I overwatered them and they got some fungal disease because of it.
So much goes into starting a successful garden but these basic tips should help you get your plant babies off to a good start.