By far the easiest way to start gardening indoors is container gardening. It is inexpensive and with the exception of soil and fertilizer, you probably already have a lot of useable containers lying around your home that you probably don’t realize.
Milk jugs, plastic soda bottles, baskets with a plastic liner and mason jars can all be used as containers for your indoor garden. Of course, there are also plenty of commercially-available options too. Window sill planter boxes are a popular way to grow small plants and herbs. More traditional ceramic containers are also an option. These containers are usually more expensive, but the large variety of available sizes make them a convenient choice for many indoor gardening tasks.
You can even make your own containers using wood. For best results, I recommend using either redwood or cedar when making your own planting containers as both species are naturally rot resistant — circumventing the addition of harmful wood treatments which leach into soil and ultimately, your crop.