As others have said, it’s possible (though very expensive) to simply build a large-enough solar-electric system to simply plug in in place of a grid connection, but this is not the cheapest way to do it. The cheapest way is to reduce energy usage first.
Existing North American houses are so energy-inefficient that there are plenty of things you can do to reduce energy use before you even touch the supply. However, some of the greatest techniques for capturing and storing energy may be difficult to implement in an existing house. This is extremely dependent on the type of existing construction, the orientation of the existing house, etc.
If you’re building new, you have a lot more freedom. And if you have not yet chosen your site, you have even more freedom. When people think of providing energy for their houses themselves, they gennerally blur two separate things: the provision of heat, and the provision of electricity.
I’ll look at heat first.
Basically, in a house, you have to provide heat, store it, and keep it from leaving. You can provide the heat via a furnace or stove, but this costs money for fuel. This cost can be reduced by capturing the light and heat of the sun through windows facing the equator (south for us in the Northern Hemisphere).
You then store the heat in thermal mass: walls or floors of rammed earth, concrete, or stone; you can even use tubes of water. Thermal mass also slows down the rate of change of temperature in a house. If you leave the door open, incoming air will be warmed or cooled to the temperature of the walls.
You seal the house, closing all those little cracks and joints, so that you don’t have to heat as much air. You have to have a certain amoint of ventilation (in Ontario, it’s 0.3 air changes per hour), but you can then manage it through a heat-recovery ventilator. Or by simply opening the window.
Lastly, you insulate the heck out of the house. Place a vapour barrier on the warm side of the insulation to keep water from condensing in the cold parts of the wall.
Such a house, capturing heat and storing it, is a solar collector. You don’t need an active heat-collection system to warm the house, because the heat is already where you want it to be.
Then there’s electricity. You can make it locally using photovoltaic panels, wind generators, hydroelectric generators, or even fuel-fired generators (diesel, for example). But these all cost.
So the same kinds of principles to reduce the planned energy usage apply. Put wall warts, and devices that never truly turn off, on power bars so that you can switch them off when they aren’t being used. Use compact-fluorescent or LED bulbs intead of incandescent. Design the house so that work areas are daylit. (Artists know about this, choosing north light (in the northern hemisphere) for its colour qualities.) Use task lighting instead of lighting a room.
And, critically, if you’re going on locally-generated electricity, avoid extensive use of anything that heats via electricity.
You’re okay with running a small appliance for a few minutes, but electric stoves, water heaters, and dryers are the three most electricity-consuming appliances in the house. Not supplying them through solar will save tens of thousands. So you get a stove that burns gas. Or wood. And you get a gas dryer. Or hang your clothes up to dry.
You can store your locally-geneated electricity in batteries, just as you store your heat in thermal mass. This gives you some leeway with respect to large electrical loads; you fill the batteries with your solar panels or wind generator over time, and then you can draw them down, for a short time, to supply a heavy load like a toaster.
By doing this kind of design, you reduce the loads you have to supply, and then you greatly reduce the costs of that supply.
