Hello, I wrote an answer here that talked about the relative size and structure of English medieval farms in the eleventh and twelfth centuries. The largest class of peasantry at the time of Domesday were villeins or 'villagers' - some 40% of the population - who were tenants responsible for on a very rough average around some 30 acres of land, spread across multiple fields. Rents or taxation were typically provided in terms of service, usually in the form of labour on the lord's own field. Monastic records in particular are fairly substantive in recording the seasonal hours provided by the lay community on monastic grounds; given that these grounds were worked collectively by the community as a whole, the burden of hours on an individual tenant is unlikely to have been too overwhelming. Further responsibilities would have been the tending of livestock, in particular the oxen for communal plough teams, sheep, pigs and cattle. Although individual tenant households were assigned specific plots, Domesday suggests that fields tended to be worked collectively by communal plough teams, in a three field rotation system.

The actual duties of a farmer of any class depended, as they do today, heavily on the season. Thankfully we have a multiplicity of sources outside of modern agriculture to tell us what those duties were. The most common sources are Books of Hours, popular religious manuscripts designed for the lay population with select Bible verses, prayers and psalms, as well as calendars of saints' days and important holidays. Many of those books produced for wealthier customers would often be illuminated, and a common theme was the agricultural calendar. These decorations could also be used as motifs in church murals or in rood carvings. Broadly speaking the activities per month are:

January: Repairs, both domestic and of tools and equipment, and weaving.

February: Ploughing and fertilising

March: Ploughing, weeding, and sowing. The start of lambing and shearing season (particularly important in areas such as Dorset and the Peaks where wool was a major cash crop)

April: Pruning, weeding, scaring birds. Lambing and calving.

May: Essentially the same as April

June: Harvesting early crops, scything grass to make hay or silage.

July: Gathering crops, ploughing harvested fields for a second crop.

August: Harvesting later crops, winnowing grain.

September: Harvesting and winnowing, milling grain.

October: Sowing winter crops, milling, weaving.

November: Butchering animals for winter, salting or smoking the meat, weaving.

December: Digging the fields, weaving, gathering flocks to winter pasture or barns.

On top of these duties, women in particular would have been busy spinning wool into yarn, primarily using a spindle-whorl until the introduction of spinning wheels to Europe in the 13th Century. Other everyday tasks would have included tending animals and the maintenance of personal kitchen-gardens, the gathering of rushes - important for the production of linen, for flooring and weaving and thatched roofs - and general household maintenance. In the quieter months of April and May, those not employed in the wool trade may have had the opportunity for other work, such as foraging and hunting or fishing.

An interesting window into early medieval daily life comes from Ælfric's Colloquy, an eleventh century Latin textbook for novices presented as a series of conversations between a teacher and various members of the community that a member of clergy might expect to encounter while about their daily business:

Teacher: Can you tell us, ploughman, how you do your work?

Ploughman: Master, I have to work so very hard. I go out at the crack of dawn to drive the oxen to the field and yoke them to the plough. For not even in the bitter winter would I dare to stay at home for fear of my lord; but, when I have yoked up the oxen and fastened the plough and the ploughshare to the plough, then I must plough a whole field or more for the whole day.

Teacher: Have you any mates?

Ploughman: Yes, I have one boy who drives the oxen with a goad. He is hoarse from shouting and the cold.

Teacher: Do you do anything more during the day?

Ploughman: Yes, indeed, I do very much more. I have to fill the stable with hay for the oxen, water them and take their dung outside. Alas, I have to endure such hard work since I am not a free man.

Teacher: Tell us, shepherd, what work do you do?

Shepherd: Yes, my teacher, I have much work to do. As soon as it is light, I drive the ewes to the pastures and guard them with dogs through heat and cold, so that the wolves do not devour them. I drive them to the folds, where I milk them twice a day. I move their folds and I make butter and cheese as well, and I am faithful to my lord.

Teacher: What did you do, oxherd?

Oxherd: I work very hard for my lord. When the ploughman has unyoked his oxen, I take them out to pasture and stand over them all night to guard them against thieves and again, at dawn, I give them back to the ploughman well-fed and watered.

Other community figures encountered include a hunter, a bird-catcher and falconer, a fisherman, a salter and a baker.

Also, I'm slightly confused by what you mean with this bit:

Did they have to do deliveries themselves, or did the Crown's soldiers do that?

Typically, most farmers during the middle ages would be serfs. They would be working on land owned by someone else, typically a noble lord or the Catholic church. Their busiest time of the year would be between spring and fall during the actual farming season. The rest of the year peasants worked what we would consider odd jobs or seasonal work.

During the growing season, they would work anywhere from 3 or 4 days on the land, to everyday during harvests. Depending on the time and place there would also be military drills once a week. England, for example, passed the Archery Law in 1252 requiring all men of fighting age to know how to use a bow. The armies of the time were made largely of levies of the local population rather than a large standing military, and it was important that those people knew how to fight in some form.

There was also Sunday church, attendance was socially required, if not by law in some places. The sabbath was held to be important during the middle ages due to the sway the Church had over political matters throughout Europe. During this time, dozens or hundreds of nearby people would meet for services, which would take place in Latin, and then spend the rest of the day around the church. Churches were the social center of the time, and many were supported by centuries of funding and were bastions of art. The Catholic Church made sure that details were intricate and showy, as most of the population throughout Europe was illiterate at this time, and the best way, they felt, to spread religion was through art. To that end, religious plays depicting scenes from the bible would take place, and music would be played or sung, commonly using local choirs.

| | TLDR: In short, farms were often smaller then we imagine today, and once the work was done, people found ways to keep busy, either through leisure or through finding other work to do around the farm.