Never re-use soil from another plant or outdoors to start your seeds indoors. This soil will carry all sorts of pathogens and possibly insects. Start with something fresh, and something sterilized to prevent disease.
Some seeds like a little soak before they get planted; beets, peas, beans, all benefit from a 4-24 hour soak before being planted.
Perennial seeds like a period of cold before being started. If you’re starting any perennial, cold stratify them for 3-6 weeks before you plant them. Take the seeds, place them in your fridge, then remove after a few weeks. This simulates the conditions perennial seeds go through outdoors during the winter, and helps break down the hard coat on the seed, giving you a much higher germination (and success rate!) when starting them indoors.
If watering seeds from the bottom up, don’t allow them to sit in standing water for more than 20 minutes. This will help protect against fungi, mould, and mildews attacking your delicate seedlings.
Sprinkle a bit of cinnamon down on your soil when you plant your seeds, or water every 3-4 weeks with a weak chamomile tea. Both act as a natural anti-fungal agent, protecting your seedlings from damping off.