Starting your own seeds at home is very rewarding, and much more cost effective than purchasing starter plants. Every seed is different, the first thing you should do when trying to germinate new seeds is do a web search for "PLANT NAME germination." It is often helpful to use the Latin, or scientific, name of the plant with this search.
The general rule of thumb is to cover seeds no more than twice their thickness in the soil. We recommend using 4" pots with a sterile seed starting mix to prevent fungal diseases. You can use soil from your garden or yard, but we recommend pasteurizing it first using moist heat for at least 30 minutes at between 160 and 180 degrees Fahrenheit. This will kill off most pathogens, but still leave beneficial soil microbes and mycorrhizae.
Seeds often germinate better with basal, or bottom, heat. You can purchase commercial seed mats, or can leave the trays of seeds on warm appliances, like the top of your refrigerator.
Some seeds need light to germinate. These seeds should be "surface sown" and not covered with soil. Lettuce is a common seed that requires light. You will find this information when you search "PLANT NAME germination."
This link from Sunset Magazine has a lot of good additional information.
Often the best thing you can do is experiment through trial and error. Some seeds might need cold treatment before sowing, others might need special treatments like smoke or special plant hormones to break their dormancy and start germinating.
If you need some free seeds to get started, send us an email at firstname.lastname@example.org and we will let you know how you can join our seed library. And here is a great blog post from Planting Justice on sharing seeds and local seed sharing resources in the San Francisco Bay area.