There are many cheap ways to start seeds. I use whatever I have on hand, egg shells, egg cartons, ice cream containers, dixie cups, really anything that will hold dirt, is biodegradable, and won't melt when water is applied will do. (See the article in Frugal Gardening about making plantable paper seed starters.)
Caring for the seedlings is very simple, I cover the sprouting plants with clear plastic to keep the moisture in. Once they are an inch high the plastic is removed and I have a small oscillating fan or two blowing for a few hours
Some of the plants will require transplanting into larger pots. I usually hang on to a few 2 quart ice cream boxes. Plastic milk jugs are good too and you can use them as mini green houses when you are putting smaller seedlings into the ground. Just flip them upside down and plop a rock on top to keep the wind from blowing them off.
When it is time to harden off the young plants I have found taking two or three weeks gives the highest survival rates. Here are my general rules:
- Set out under a cold frame on a wet, overcast day - no high temperatures in the afternoon and low chance of hard frost at night.
- Limit direct sunlight at first. As you harden them place them where there is afternoon shade.
- Once in the ground keep an eye on the weather in case there is a late frost.
- Keep extra seedlings available in case you need to replace failed plants.