Organic gardening has become a very mainstream, popular method of growing food. Conventional plants and vegetable seeds, seedlings, soil and soil amendments have likely been treated with chemical pesticides and/or contain genetically modified organisms. Gardeners looking to avoid pesticides and GMO's will find a wide variety of organic garden products available on the market.
Many brick and mortar stores now offer organic seeds for sale, and with a little research, it may be possible to find a local organic farm that sells vegetable or herb seedlings. Organic Gardening has a great list of companies that offer organic seed varieties. Purchasing certified organic seeds ensured that the food that you harvest will be organic as well (as long as the plants are not treated with any kind of chemical or pesticide.)
To treat pests in an organic garden, except from preventing them, the go-to method is with a soap spray made of 1 tsp. castile soap, 2 tsp. oil (vegetable,) and water. Crushed hot peppers or garlic and onion can also be added to the mixture to repel insects. This all purpose spray is an easy, inexpensive and effective way to organically get rid of pests in your garden.
For more information on Organic Pest-Control Techniques take a look here.