Those little containers are just the center cores of paper towel rolls. I cut them into thirds, tie them with the sisal twine (to hold them or else they start to unravel when they get wet), fill them with moistened sterile potting soil and then planted my seeds. They are all sprouting (I should take a new picture) now. When they are big enough, they'll either go into the garden or into larger pots (depending on what they are and the timing in relation to our last frost date). They can be planted, core, twine and all!

The tray with the lip is so that I can water the tray and not the seedlings. This way, they develop better root systems as they grow downward to get to it. Plus, it keeps moss/mold development at the leaf end to a minimum.