Prefab Greenhouse + Ardunio Controls = Automated Agriculture (Video)
Sam Bagot and Will Bratton operate Horto Domi (hortodomi.com), an agricultural project they describe as "beyond organic." They're working with small prefab greenhouses, adding sensors and Arduino-actuated controls, and even including an earthworm breeding area in most domes, because earthworms are good for the soil and can increase plant production. If you're the kind of person whose plants always seem to shrivel up and die, this may be a great way to garden. With watering and other functions automated, it looks like all you have to do is set your controls, plant what you want to grow, and wait for the "time to harvest" alarm to go off. Okay, it might not be that simple, but Sam and Will say their gardening method saves a lot of energy and time. It also looks like fun, besides being an easy way to grow your own 100% organic fruits and vegetables.
I'm in the Pacific Northwest (PNW), so my two main sources of information are these two books by Steve Solomon and Carol Deppe. Depending on your climate Elliot Coleman has good advice. I don't know about other climates. I'm using organic practices, so my advice isn't useful for those going the conventional route.
In the PNW the ground doesn't freeze, so some microorganisms aren't killed off like they are elsewhere. This means after gardening about three years in the same spot the ground becomes far less productive. So... best practice is to let the ground lie fallow for a year to starve out the bad microorganisms, which increases your land requirements.
Replenishing the soil in terms of fertilizer can be challenging if one is going the self-sufficiency route.
Raising meat requires add'l land, and coming up with self-sufficient animal food requires even more land. I'm raising poultry and find that in my climate ducks are the most self-sufficient, followed by geese. Goats are able to forage a bit. I do pigs, too, and while they do forage and consume all our scraps, they require external feed.
We are simply not able to grow certain staples such as rice. We're gluten-free, so wheat is out for us, but anyone trying to be self-sufficient who consumes white flour is in for a hard time. If growing grain, do you count fuel in your self-sufficiency? If not, are you using oxen?
Given our family's needs, I think three-four acres would do it (taking rotation into account), but we're not aiming for total self-sufficiency. This assumes shipping in animal feed. That said, I think fruit trees can be a significant source of food without requiring a bunch of input.
Given the realities of property taxes I don't think self-sufficient farming is possible except in areas well away from population centers where land/taxes are dirt cheap. It also takes a lot of work. There's a big learning curve, too. If you're thinking about raising your own food, get started (even on a small scale). This isn't something you can pick up by reading a few books...