How much food do you need to grow? For your own family, you can till and prepare enough soil with a pick and shovel. If you plan on sharing your harvest with multiple families, you probably need a horse or ox to pull a larger plow. Depending on the crop you select, you can probably plant enough seed or starter plants by hand. Harvesting is another time when you will need to some help to get all the crops in. If you grow grains, you will have to cut, stack, dry, thresh, and store the grain. This can be done by hand, or with hand tools (a flail to thresh grains) without needing powered equipment.
As a mental exercise, pick a 20' x 20' section of your lawn and imagine what you would need to do to turn it into farmable land. Dig up all the grass or till it under, test the soil for acidity and add lime or sulfur to balance the Ph, fertilize with animal manure, plant something (example wheat), irrigate it, harvest it with a scythe or sickle, thresh the grain, then store it. No modern equipment is indispensable, but it still takes a LOT of hard work.