Yes, you can have a self-sustaining homestead that gives you all the food you need to live. So, hear me out, because as long as you have an acre of land, you can do this.
Surprisingly, you can get more off your 1-acre farm than a 10-acre farm can deliver using commercial farming methods by using these techniques.
Incredible, right?
And no, you don't need to have livestock to make this idea work. But if you don't mind taking that route, your options include cows, pigs, hens, and even goats.
But I'll assume you have decided to include livestock in your plan, just to make sure no one is left out here.
So, Let's Assume You Have Decided To Get A Dairy Cow

You have to know how to take care of it. A cow will give you milk, meat, and manure; not necessarily in that order.
I should let you know that keeping a cow is a little bit of an expense. But if you can afford it, worry not, you will get all that money back by the time the year is over.
Also, don't worry too much about milking, the process takes under 10 minutes.
However, it should not seem like you must have a cow to make a self-sustaining farm. However, this animal will make your work a lot easier.
With an acre farm, you will have to devote about half of it to the cow's pasture.
Once you plant the grass you need, you have to wait four years before you can rotate it with crops.
For best results, you should rotate crops with each quarter of an acre of grass every year for the best productivity throughout the farm.
Also, you will need a rotational grazing to avoid overgrazing. But half an acre should be plenty, and there might be some grass left over that you can turn into hay.
You can keep the cow inside during the winter, only letting it out for some fresh air every day.
Then You Will Need An Edible Garden, Or Several

This should take about half an acre separated into four different sections which allow you to rotate your crops throughout the season.
An example of great crop choices under this method would be 1) potatoes, 2) legumes such as peas and beans, 3) brassicas (cabbage family), and 4) root vegetables such as carrots and beets.
Each of these crops should go on a single plot, and with every season, they should be rotated and grown in a different plot, including the plots used to graze the cow. The manure the cow generates can be used to keep these plots fertile.
That's Pretty Much It
See! Even with a small area, you can still have a self-sustaining farm that gives you milk and food, including meat, depending on the kind of animals or poultry you decide to keep.
So, if you have been toying with the idea of not having to buy your food from anyone, this is how you turn it into reality. Good luck!