In dogs, heart failure is usually characterized by problems with the mitral valve. This is especially true of smaller breeds, but is applicable to at least some extent with all dogs. The mitral valve refers to the muscular valve that separates the left atrium and ventricle. Its function, when working properly, is to prevent the back flow of blood once it has passed through one section of the heart to increase the efficiency of the heart's pumping, i.e. - each portion of blood that passes through the heart only needs to be pumped once because the mitral valve prevents it from flowing backwards. Over time, however, this valve begins to shrink and harden as a natural consequence of aging. When this occurs, the seal it forms is no longer as tight as it needs to be and blood is allowed to flow backwards, thereby greatly increasing the pressure in the left ventricle which now has blood flowing in from two sources. At worst, this condition can lead to increased blood pressure throughout the entire body, including the lungs, brain, and other organs.
The ultimate result of living with this increased blood pressure is that your dog's blood will begin to leak out of the blood vessels carrying it and absorb into surrounding muscular tissue. This causes an uncomfortable and noticeable swelling called edema. An early warning sign of this that you should take very seriously is a persistent cough not related to a cold or other transient illness. Though it can be relieved through the use of diuretics which make the dog urinate more and thus relieve some of the pressure of excess bodily fluids, edema is really just a symptom of the greater underlying problem: the insufficiency of the mitral valve.
As time passes, even if the symptoms are treated, the higher strain being put on the heart to pump the blood as well as the elevated blood pressure will cause a thickening of the heart's walls. Eventually, it will be unable to meet the burden placed upon it, and it will fail.
However, the situation is not without some degree of hope. Though mitral valve heart disease is really just a natural consequence of aging, if you spot the warning signs early on, there are many steps you can take to significantly slow (if not stop) its progression. In particular, there are medications such as digoxin and various ACE inhibitors that will help to bring a natural rhythm back to the heart muscles and reduce the overall strain on the organ. In addition, switching to a specially-formulated pet food that is low in sodium and engaging in a veterinarian-prescribed exercise program will help to naturally reduce blood pressure and increase the capacity of the heart to deal with the burden placed upon it by mitral valve failure.