Passive solar design is worth books full of calculations and design principles, and when done thoroughly and correctly can provide up to all of your home heating and cooling--completely and utterly dependent on where you live and how intensely you pursue passive solar design goals.
It generally doesn't provide all, unless you're die-hard about living with nature you'd want a backup anyway, and in what I call the "upper Southeast" (US) climate, you can also very easily mess it up and create a house that is way too hot in the summer. Many customers at my job are building in this climate and have heard a thing or two about passive solar, so they stick a bunch of windows on the south side of their house and say to themselves "hey, we're passive solar!"
Which is going in the right direction, because to get some benefit you don't have to be all or nothing...but they probably don't realize they're still going to be heating and cooling their houses primarily with a conventional mechanical system, and so the delusion that total benefit requires minimal effort must be dispelled, diplomatically, by me.
The idea of passive solar design is simply to realize that the placement of your house within its surroundings has consequences, whether you care to think about those consequences or not, so you might as well think about them use them to your benefit. There is energy floating around out there, solar folks call it "insolation" and it is measured in kilowatts per square meter, and it exists in measurable amounts daily just because of sunshine. If you don't have a photovoltaic panel it is generally too diffuse to do much with (although plants love it and consequently life on earth up to and including our fossil fuel driven economy can exist), but it turns out that glass too is very adept and letting it pass through in one direction much more quickly than it lets it escape in another.* This means a glass box can hold heat for a while; indeed, this is why your car gets very hot in the summer, and this is what passive solar wants to harness by thoughtfully placing your windows. Certain windows are specially designed for this: two- (or even three-, four-, five-) paned and filled with inert gases to reduce conduction heat flow out, but also covered in coatings on the outside that help radiation heat, that "insolation", come on in. You put these windows on the south side of your house and put as few windows as possible everywhere else. Since the sun's arc is always slightly southward in the sky if you live here in the northern hemisphere, facing south gives you the most opportunity for the longest period of direct sunlight.
But passive solar is not just windows. For one thing, the sun's out longer in the summer than in the winter, and if you got direct sunlight all day long in an already hot summer, your house would begin to resemble that hot car in which dogs and babies die every year. I've seen a couple who wanted to go "passive solar" stick a south-facing glass room off of their living room, with glass roof as well, and they admitted that in summer that whole wing of the house was intolerable. You want all that sunlight entering your house in winter only, and this is easy to accomplish with correctly sized overhangs. The sun's path is much higher in the summer than in the winter--that's why it's out longer, and also the bulk of the reason why summer is hotter than winter. (The variation in our physical proximity to the sun in summer verses winter is too small to have anything to do with it.) It turns out the more parallel to an energy source you are, the more kilowatts per meter-squared you can intercept. Like shining a flashlight beam right at you or catching the beam at an odd angle. In winter the sun is lower, you're not at as ideal of an angle, and you get less kilowatts per meter. This means less of that "insolation" is around in winter, but still enough to help you heat your house. So build longer overhangs, long enough to block out the sun when it's high, but short enough not to block the sun when it is low. The further south you go the longer they need to be; two feet long is ample in the upper Southeast. (Flip this if you're in the southern hemisphere.)
However, even the right overhangs and the right windows are not enough, especially when the temptation is to just throw in as many south-facing windows as you can. Witness the couple with the glass room. An overhang and for heaven sakes a real ceiling would have helped them, but they still might have overheated, because a lot of heat can still pour into those windows in the winter, and after a certain "saturation" point, there's nowhere for more of it to go except to keep hanging out in the air, raising the temperature. Yet at night, all that glass, which no matter how high-tech is still is utterly pitiful at slowing heat conduction (aka insulating), is sucking the heat right out, and your heating apparatus will work overtime to make up the difference.
This does not have to be! There are quite a few materials that are excellent at storing heat. Water is the most amazing and crucial example, since oceans absorbing heat and releasing it at opportune times have a lot to do with the fact that our planet doesn't flip between daytime oven and nighttime ice bath like, say, Mars. Concrete, stone, brick, or tile are nowhere near as prodigious at heat storage as water but are still much better than air; even drywall is pretty decent. Passive solar homes will often employ concrete slab floors, either covered or uncovered with tile, build large brick or stone fireplaces in the direct path of the south facing windows. I've heard of designs where people stick in decorative columns filled with water (just use an aquarium?), but that should be used with caution since one of those failing would have disastrous consequences for the durability of your living room. These materials absorb the extra heat coming in from the windows and allow the room to remain a pleasant temperature, yet also release the heat back out slowly, well into the night, supplementing the work your fossil fuel heating apparatus will need to do. You do need to get the ratios right but fortunately physics and engineering have the tools to tackle this problem: there are formulas and rules of thumb for how much glass, how much "thermal mass", etc. for your climate and home size.
People who are really crazy about passive solar and green building in general have built houses out of old tires rammed with dirt in the middle (tires and earth are great at absorbing and holding heat), covered their south wall with super high-tech windows, done the correct overhang thing, and eschewed any conventional heating and cooling altogether except for backup. These "earth ships" work great in the desert Southwest where it's always sunny and huge temperature swings between night and day are a problem. I've seen a house like that here, but it's a little harder to get right.
Another important component is good insulation in the rest of the house. This is always good anyway, because once you get heat into your house by whatever means you get it there, you're gonna lose it eventually, because conduction always happens. The "more" insulation (the better the R-value), the slower you will lose heat. If your heating apparatus is the sun (barring cloudy days, why you still want a backup), it "comes on" at regular intervals you can't control but can predict, and if you can use thermal mass and insulation to time your heat loss within those intervals to remain comfortable, then hey. That didn't cost you anything in energy inputs. Obviously there are too many variables to get this perfect, especially considering outside temperature changes and conduction happens much faster when it is much colder outside. But more insulation pretty much always helps.
The last important feature in passive solar, which many people don't think of, is the layout of the house itself. If the south side of your house is warm and full of thermal mass and the whole thing is insulated above and beyond what code requires, still you're not doing much if your house is long and skinny along the North-South axis. The heat you're gaining on the south side just isn't getting to the other side of the house.
In any climate that gets hot in the summer but cold in the winter, you have to get the balance of heating and cooling features right. Here, I've noticed, because we must spend about four times as much energy on heating than on cooling, we tend to design to be warm in winter, forgetting that we have to think about how to be cool in summer. The humidity of this climate makes it worse, because humidity makes even moderately warm temperatures feel miserable. There is honestly nothing quite like an air conditioner for making a house feel comfortable because it dehumidifies, just as a consequence of how it works. Humidity is also hell on houses, and mold issues abound in this climate in poorly designed and un-air-conditioned buildings. There is a growing school of "green" thought which supposes that durability is the most important component of sustainable building, because however energy efficient or non-toxic something is, if it breaks in a few years and you just have to throw it away and keep buying new ones, that's still impacting the environment in a bigger way than necessary. I agree that houses should be built to last centuries if possible and homeowners should not have to deal with their beautiful passive baby succumbing to terrible mold issues; some form of dehumidification is critical to a truly sustainable home in this climate. Since you ought to have a backup anyway that may well be an heat pump/air conditioner system, properly sized to your cooling load, not your heating load, and used minimally in conjunction with other methods. There are probably ample "passive dehumidification" methods that I just don't know much about, and they might work will with proper design; I assert that moisture around here is ubiquitous and ignoring it a serious design flaw. Passive dehumidification endeavors must be an extremely difficult one to get right, and in light of durability concerns an air conditioner for dehumidification isn't necessarily such an un-green choice.
*The physics of this involve the difference between conduction and radiation, but also how the molecules in materials interact with radiation and then release it again. It's fascinating, but not short. The thing you should know is that "conduction" is heat moving from hot to cold, as it does, through things in physical contact. Meanwhile "radiation" is heat associated with wave stuff, which has it's own complex set of rules not immediately discernible from our interaction with the real world in the same way that conduction is. Anything above 0 Kelvins radiates electromagnetic waves of certain wavelengths, the hotter, the shorter the wavelengths, and infrared radiation coming from both the sun and us is commonly referred to as a form of heat.