The quickest and easiest way to start growing and eating your crop is to Grow Sprouts in a Jar.
Growing lettuce and other greens in a tray or cup by the window works. Be sure to space out your seeds. That little seed will grow into full-size lettuce if you give it room, water, and sun.
Start your tomatoes, peppers, cucumbers, peas, whatever else you want. Grow them in old pop bottles, plastic dairy containers like from sour cream. Be sure to water and keep them in a sunny place and you're good to go. If you want to up your production there are is a wide range of indoor grow systems available.