Any fruit or vegetable you buy comes with complimentary free seeds or a pit. Save the seeds to your favorite produce and use them to start your garden. Squash, cucumber, peppers, cantaloupe, and tomato seeds are some of the easiest to dry out and plant.
Ask your friends and family to save seeds from the fruit and vegetables they eat, as well. If there's regional produce they eat, but you can't find it in your local grocery store, ask them to dry out the seeds and send them to you.
If you want to plant an herb garden, your spice rack is a good place to start. Try planting several coriander, fennel and dill seeds.
Do a seed trade with neighbors or other gardening friends. It's likely they have some extra garden seeds they could spare to give you. Most vegetable seed packs you buy in the store come with far more than what you'd need for a backyard garden. Offer extra seeds, you have stashed away, as a trade.
If you can't find a nearby gardner willing or able to trade seeds with you join an online seed swap. Seed exchanges let gardeners post their needs on bulletin boards along with the free seeds they have to offer. You'll be notified when there's someone willing to swap. Garden.org has an active seedswap program.
Search the internet for gardening programs that offer free seeds. Many of these programs are geared toward community organizations, but there are some like wintersown.org that offer free seeds to individuals who request them. The only problem is you often can't pick the type of seeds you get or how many you receive.
Take advantage of seed catalogs that offer free seed packs to customers who meet certain criteria. Many companies will send you a pack or two of free seeds if you order $25 from their catalog.