Seed packets will usually have germination instructions on them for the optimal conditions. Some need total dark, some need strong light, some need high humidity, etc. When sown you can do your watering with a spray bottle when needed and saran wrap to help keep the moisture in. Watering from below is fine too, but do take them out of your tray as Carlos suggested, or you're at a big risk of them staying too wet, which can lead to big problems.

After they've germinated, you can generally let them get a little dry in between waterings. Staying on the dry side is usually safer than staying on the wet side and probably more seedlings are killed by 'kindness' (overwatering) than any other way. I know that's my method of choice for sending seedlings to the compost pile before their time. Check the individual requirements though!

For many plants you can sow a bunch of seeds in the same pot, pretty tightly packed together. Then transfer them to individual containers as they get to be a few inches high. This depends on what you're growing and how much space you have available though.

There are also quite a few veggie plants that can be sown directly into the ground depending on the length of your growing season, this should work for standard green beans.