The first part of farming is planting the seeds in good dirt, so they can begin to grow. In most parts of Europe, North Africa, and West Asia, early farmers planted their seeds in the fall, around October.
You can plant seeds one at a time, digging little holes, but usually people used a plow.
Mostly men (though not only men) did the plowing, because you have to have very strong arms to lift and push the plow. Women often walked behind the men, dropping the seeds into the furrow made by the plow. The main kinds of plants that people planted were grains: wheat, barley, millet, oats and rye, and legumes like peas, lentils, and chickpeas.
People also planted trees, especially fruit trees and olive trees, and grapevines, but they didn’t plant the seeds: they planted small branches from other trees, and these grew into big fruit trees or vines.
Most people also had a small vegetable garden, for onions, cucumbers, garlic, spinach, lettuce, cabbage, and herbs like rosemary, oregano, thyme and mint.
Bibliography and further reading about farming:
Ancient Agriculture: From Foraging to Farming, by Michael and Mary Woods (2000). For middle schoolers, with plenty of information about how farming got started, and how it worked.
Ancient Greek Agriculture: An Introduction, by Signe Isager and Jens Erik Skydsgaar (1992). Details of what tools farmers used, and what methods.
Famine and Food Supply in the Graeco-Roman World : Responses to Risk and Crisis, by Peter Garnsey (1988). By a leading specialist in Greek and Roman food and farming, and not too hard to read. Especially good on crop failure.