I collect egg containers all year long because they are absolutely perfect for starting seeds. If you haven't been collecting them you can always buy some containers at a garden store, or just buy decomposable paper cups. I dunk them in water because the seeds will need a lot of moisture to germinate.
Add your dirt, place the seeds in a tiny hollow (most seeds will need only about 1/4 in of depth) and cover them up. Place them in a south facing window. At this point in the year I have cauliflower, broccoli, some greens, leeks, and onions starting indoors. I will plant more later outside to have a constantly supply inside of everything being ready for picking at once.
I plan on putting out more greens like spinach, strawberry spinach, kale, collards, etc as well as my peas the first week of April. These seedlings will probably be ready to go into the cold frame a week after that, and after another week I'll plant them in the ground.
Be sure to mist daily and water about once a week. I just put towels under then this year, but I've also had good success putting a lipped baking pan under and just watering them by pouring water into the pan.
Just leaving them in the sun I've had several sprout, but I want the rest to hurry so I put up a florescent light. You can buy special "growing" lights, but just a regular cheap light will work.
The "set-up" with the light propped up on books. I always think this is a bit sloppy looking for the several months it'll be there so I put a cloth over it. Just be sure the cloth doesn't block out the window's light.
There you go! Super easy, super cheap.