Walmart, target and other large retailers offering food delivery services were offering big sales for delivery only. Not certain whether the trend will continue into the future but it was nice while it lasted.
edit:
Learning to hunt and fish
Give a man a fish, and you might feed him for a day. Teach a man to fish and you could feed him for a lifetime.
While it seems that hobbies like hunting and fishing are on a decline. Perhaps current era food prices are exactly what they need to make a return?
Foraging in the wild
There are places in the wild where fruits and vegetables grow naturally. Some are located close to official hiking trails and natural landmarks like waterfalls.
Working part time in the food industry
The food industry is known for sometimes giving away free food and cost benefits. Bakeries and restaurants and known for throwing food away. Which employees sometimes are allowed to have.
....
What are other good methods of cutting costs on food items?
Shopping around, paying particular attention to the prices of certain items in different shops can add up to a huge difference over time, but in can vary so much based on the country your in and the different competition available. Saying "stick with Amazon" might be an ok strategy in the middle of nowhere in America, but in Europe you would now be overpaying based on the jacked up prices they seem to place on things. One other important thing: Pay particular attention to the special offers that you are picking up, this may be more of an issue with specific retailers, but several times lately I've caught special promotional items not coming up with the right price when you come to pay and having to tell them to fix the price to what is advertised.