One of the easiest edible plants to grow indoors is various types of herbs. Depending on how many you plan on growing depends on the size of herb container you will need. You can use a planter made specifically for this or you can use a bucket.
If using a bucket you will need to carefully drill holes in the bottom, then line the bottom with 1-2 inches of gravel or rock (this is so that water can drain out), then fill with your planting soil before planting your herbs. Underneath your bucket you will want to have a planter tray underneath to catch any water that may come out when you water your herbs.
If you are a beginner you will want to start with the easiest herbs for growing indoors.
The Bay Tree: this one is a slow grower. The best type of bay tree for cooking with is the Laurus nobilis. Do not let your bay tree get too dry or it can become infested with scale. If this happens use a dishwashing detergent to wash the leaves off and be sure to rinse them well.
Chive: The best variety of chive to grow inside is the Grolau. Chive is an easier herb for growing indoors as it does not require as much light as other herbs do.
Lemongrass: Your lemongrass doesn't actually need soil to grow. If you get a stalk at the grocery store or market that has a lot of stem and an intact bottom you can just trim the top, place into a container with a couple inches of water and watch it grow. Your lemongrass should start growing new roots and sprout out several new stalks from the bottom.
Mint: You will want to grow any type of mint in its own herb container as mint tends to be an invasive species of plant.
Parsley: Like the Chive it does not need as much sun to grow, however, parsley tends to be another slow grower and may not yield a lot.