This is an awesome question. I am going to be taking an entire class dedicated to answering that question next semester. Transportation planning in suburbia presents several important challenges, and I will attempt to summarize the most important of them as best I can.
The first issue is a question of origins and destinations. The easiest way to explain it is through a picture. In this picture, orange dots represent origin points (residences) and green dots represent destinations (places of employment, shopping, etc.). The possible scenarios are one-to-one (top left), many-to-one (top right), one-to-many (bottom left), and many-to-many (bottom right).
In the one-to-one scenario, everyone lives in one district and works in another district (one-to-one meaning, then, that there is one origin and one destination). For a situation like this, a light rail system is the most appropriate transportation response. Light rail is extremely efficient at moving large numbers of people along one specific route, but it is also very expensive and inflexible.
The many-to-one scenario is the model originally envisioned for suburbia, where jobs are located in the central city and residences in the periphery. The one-to-many scenario is simply its inverse (imagine a farming community where everyone lives in town but works in the fields). In a situation like this, light rail is inefficient. Buses are the proper mass transit choice. While they can't carry as many people as quickly as light rail, they are incredibly flexible and much more easily subdivided, as well as being much cheaper.
The final model, the many-to-many scenario, best describes the typical American city of today. In this model, residences and destinations are mixed throughout the community. Furthermore, the distribution is more or less random—there is no guarantee that the person living at one particular green dot works at the nearest orange dot, or even a nearby orange dot. In such a situation, the transportation outcome is chaos. Light rail is obviously useless. Even buses are inefficient, though, because each bus would carry only two or three people—it would be no different from a car.*
Of course, these are all models, not perfect pictures of reality. For the most part, I think reality falls somewhere between the many-to-one and many-to-many scenarios, and in any case it's far more complex than any of these models allow. However, the models serve to provide a simple illustration of a complex subject.
Another factor affecting mass transit is population density. The easiest way to illustrate this is by looking at extremes. If you have a city with a thousand people living on each block, then you can intuitively understand why mass transit would be appropriate. On the other hand, if you have a rural area with one residence per square mile, you can intuitively understand why mass transit would be laughable. In order to have mass transit, you have to have masses. As population density increases, the efficiency and efficacy of mass transit also increases. One study I found indicated that mass transit efficiency improved most dramatically once a city reached 20 residences or jobs (origins or destinations) per acre. Provo, by comparison, has a population density of about 4 people per acre. This obviously doesn't take into account jobs, but it is still far below the threshold for optimal transit efficiency.
Even assuming that both of these difficulties have been overcome, one additional major hurdle remains. When people choose between transportation options, they base their choices on factors such as speed, convenience, price, and comfort/safety. In the low-density, auto-oriented city, often every single one of these factors will favor cars. Given ample parking availability and low congestion, it will always be faster and more convenient to drive your own car directly from your home to Wal-Mart than to walk to a bus stop, wait for the bus, get on the bus, wait as it winds through town, and then get off and walk the last half-block. Mass transit has an almost perfect safety record (especially when compared to cars' 34,000 fatalities per year), but we're so used to traffic accidents and so mesmerized by incredibly rare bus crashes with a 40-person death toll that this is easily forgotten. Moreover, in your own car, you don't have to worry about the sketchy-looking and vaguely smelly guy sitting next to you (who, again, probably isn't any real threat, but we forget this). And since mass transit programs often have to defend their existence by paying for themselves (something you never hear about our fabulously expensive roads), the cost is often at least equal to the cost of driving. When my wife still worked in Salt Lake City, she found that the cost of gas for the commute was pretty much equal to the cost of a round-trip Frontrunner ticket. In order to take the Frontrunner, she had to be at the station at a specific time and walk several blocks after getting off in Salt Lake, and the whole commute took almost twice as long. It was mostly the stress of driving on a highly congested freeway that tipped the scale for her.
It is the last of these three sets of impediments that is easiest to resolve. One simple way to boost mass transit ridership is by making mass transit nearly free, just as the sidewalks and roadways are free. (A nominal fee is often necessary to prevent abuse of the system.) Another important step is the regulation of parking. Written into most cities' zoning codes are requirements for sufficient parking for each building, often with a very expansive definition of "sufficient." The problem with free parking is that there can never be enough. To paraphrase a line from one of my textbooks, if you offered a lifetime supply of free pizza to everyone in a city, would there ever be enough pizza? A common solution to this problem is the regulation of available parking with parking meters.** This increases the cost of driving in terms of both money and convenience, providing another incentive to switch over to transit. I could name more specific solutions, but I think you get the basic idea: increase the cost (in time, speed, or convenience) of driving and decrease the cost of taking mass transit to provide incentives to switch.***
The other two issues, density and origin/destination, go hand in hand. The problems of a many-to-many system vanish when this system occurs over only a few blocks, or when there are so many origins and destinations that the picture from my example would be a solid mat of orange and green. In such a situation, the population is dense enough that a bus system could operate at high efficiency and still drop each person off within a block or so of their home and job. Parking at such a density would be prohibitively expensive purely by the laws of supply and demand, and although buses wouldn't be a perfect substitute for cars, walking would very easily fill in the gaps.
Of course, resolving the problem by significantly boosting population density avoids your question by eliminating suburbia altogether. Whether or not this is a desirable outcome is basically a moot point, because I think we can all agree that (at least in the foreseeable future) this is never going to happen. Nearly every aspect of every city in the United States that has been built in the past half-century has been designed for cars, and we can't expect to undo that. We have to work from where we are. We will always use cars here. The question is how much and in what capacity.
One promising area for improvement is mixed land uses. A perfect local example of this is South End Market, across the street from Campus Plaza. It doesn't have the selection or prices of a Wal-Mart, but it has something else—for many BYU students, walking from home to the market takes less time than walking from the edge of the Wal-Mart parking lot to Wal-Mart. Such stores, like public transit, require a certain level of population density in order to draw in a sufficient customer base without requiring them to drive, so they would function best in high-density areas like student apartments or medium-density areas like duplexes or row houses. Campus Plaza provides another example of such mixed uses, with a pizza place and a barber shop on the ground floor.
Another issue, tied to this, is a shift away from the assumption that every person needs to live in a single-family home. In reality, singles, young or small families, and empty-nesters are often best served by medium-density housing that puts them in closer proximity to other people and relevant services. Likewise, those who cannot afford cars or do not want them would stand to gain significantly from medium-density housing.
The proliferation of medium-density housing is desirable. However, in order for it to work, it has to be made appealing. When a family chooses a medium-density home over a single-family home, they are sacrificing nearly all of their yard and much of their livable square footage. For them to make that sacrifice, they have to get something in return. Part of this can come from proximity to services and entertainment facilities. It must also include parks and other outdoor recreation areas to replace the private park that is the back yard.
Cycling and walking should be both encouraged and protected. Minor streets should be narrow, with frequent stop signs, to avoid wasting space and encourage motorists by structure rather than by law to drive at safe speeds. Major streets should have bike lanes, which should be located between parked cars and the curb so that parked cars form a physical and psychological barrier protecting cyclists. They should also have planted medians, which serve the dual purpose of making streets aesthetically pleasing and providing a safe pedestrian island at crosswalks. Cityscapes in general should be designed to be pleasant for the pedestrian to walk through, with shade, visually and audibly attractive features, and sufficient protection from car traffic. The city should encourage institutions and events that draw people out of their private world and into the public realm.
I have so much more that I would love to say about this, but this answer is too long and too overdue as it is, so I"ll leave that for another question. Please, feel free to ask as many follow-up questions as you'd like or email me for ideas for further reading. This is what I expect to spend the rest of my life doing, so I have plenty more to give you.
*One possible solution to this would be something I saw on my mission in Santiago, Chile, where by my estimate only about half of the population owns cars. "Colectivos" are somewhere between a car and a bus, perhaps best described as a fixed-route taxi. They nicely solve the problem of too few people for a bus route, but they give the rider no real advantage over driving their own car. In a society like ours where everyone owns a car, such a system would likely never get off the ground.
**Spoiler alert: The city of Provo is in the process of doing a comprehensive review of parking policy, in coordination with BYU, UTA, and a variety of other entities. The review is spearheaded by an outside consulting group, which has been told that every possible solution is on the table. Also, in a development that may be related or may be merely coincidental, BYU is currently reviewing a proposal to charge parking fees for on-campus parking, which will hopefully help convince people who live three blocks from campus that it really isn't necessary to drive. My source tells me that this will be going before the faculty senate sometime in the very near future.
***Lest anyone complain about the injustice of such a move, I'd like to point out that the true cost of driving is much higher than the cost borne by the driver. For example, drivers are not made to pay for the environmental, social, or economic effects of the Wasatch inversion. (To understand the economic cost, imagine that you're a business owner who has never been to Utah before and visits in the winter to evaluate a potential regional headquarters site. If your first and last impression of the region is an ugly and barely breathable urban haze, you'll be that much more likely to choose to locate somewhere else.) Moreover, cars are dangerous. And while safety advancements have made them much safer for drivers, they have done nothing to make them safer for pedestrians. Even the fastest, fittest person stands no chance against two tons of metal moving at 35 miles per hour. In industries like construction or mining, where employment presents a risk to the employee's life, employees are given extra hazard pay. But in the business of walking or biking from one place to another, the hazard is there, but motorists pay nothing. Simply put, cars create externalities, and somebody has to pay for the externalities. It is only fair that that somebody be the motorist.