The farmers markets is one way.. buying local stuff helps you keep your spending levels low.. Growing your own salads could be fun and very economical. Freeze stuff when it is cheap.. though I don't care too much for the last tip.. I hate frozen stuff and like to buy my veggies and fruits fresh.
Sometimes conventional fruits and vegetables are more expensive if not as expensive as organic ones. The best way to save on healthy food is the same as other foods, buy on sale and buy in season. Some cities have programs where you can buy locally grown produce in boxes on a weekly basis. These are usually administered by a co-op or a farmer's market. If you have a large family you can also save by buying in bulk.