The formation of these acids is a natural process that is important in order to keep the atmosphere free of the many different types of gases, and purifying the air on a continuous basis. Just like the formation of the acid, neutralizing it and coping with its effects are also natural. The only true problem lies in the quantity, as just a fraction of the current amount is easy to cope with.
To first solve the problem, it is important to eliminate the primary sources (as the natural secondary sources aren't the true problem). This can't be accomplished by simply removing all aspects that rely on fossil fuels. Such a scenario would remove too much of society and set efforts of control further back than leaving things the way they are. What's more important is switching society's reliance to another form that can replace the power plants, the fossil fuel reliant cars, and other applications.
Already there is a large movement to accomplish these tasks. Renewable energy is on the rise all over the world, replacing coal-burning power plants with wind, wave, undersea current and hydroelectric generators, as well as solar panels and geothermal energy. Nuclear energy will provide the bulk of electrical needs until the efficiencies and affordability of the renewable energies reaches a better state. Electric cars are becoming better for keeping charges for longer distances, and soon the rechargeable vehicles will draw electricity from the above mentioned processes. Other cars that use fuel cells and bio fuels (although not that different from fossil fuels) will dramatically reduce emissions that contribute to the formation of acid rain.
Finally, in order to neutralize the current threat of acid rain, there are options to reduce the damage by reducing the acidic level. This can be accomplished by adding more base pH leveled items in areas that are heavily affected by the acid, in forests or cities, and the acid content can be brought down to a level much closer to water. Risks of the extra base pH levels will have to be assessed in order to reduce the effects from too little acid in the rain water.