I like your advice regarding visiting the farmer's market. I went today, and got some great deals on produce. I paid $1 each for a bunch of celery, 2 baskets of tomatoes, and 1 head of broccoli. These prices were much lower than what I would normally see at the grocery store, so I was very excited to stock up on these fresh produce items. Also, by supporting local farmers and businesses at farmer's markets, you are supporting your local community. When you buy locally, everyone wins.
My method for saving some money is to install a couple of sale tracking apps on your phone. I have one for my local super market which let's me know in advance when the sale is going to occur. I then align my trips to the store accordingly.