FPV is an uneveloped virus, which means that it is very resistant, and can survive for more than one year in the environment. An infected cat will shed virus in all secretions including feces, urine, and saliva.  A cat which comes into contact with secretions from an infected cat has the potential to become infected either through ingestion or inhalation of the virus. If a pregnant queen becomes infected with FPV the virus can pass through the placenta and infect the kittens in utero.  There is also some evidence that the virus can be passed via arthropod vectors, such as fleas.

FPV is a simple single stranded virus with no genes to make DNA polymerase, which it needs to replicate itself. Thus for FPV to replicate it requires cells which are mitotically active and therefore have an active DNA polymerase. Actively dividing cells include those in the bone marrow and intestinal crypts.
When FPV is ingested by a cat, it enters the lymphoid tissues of the oropharynx. FPV binds to transferrin receptors on the surface of cells. The receptor and attached virus are endocytosed, and the virus is released when pH drops. In the lymphoid tissues it replicates, and forms new virions. When the virus enters a cell it prevents that cell from starting mitosis, and eventually the cell will die releasing virus into the blood. The virus travels free from cells in the blood, and goes to other locations within the body to infect new cells.
In a cat, the most common sites for the virus to infect are the bone marrow, lymph nodes, thymus (if it has not yet involuted), spleen and cells of the intestinal crypt. These locations lead to the clinical signs associated with FPV that can be found here.
When a fetus becomes infected transplacentally there are more mitotically active cells available for infection. If this occurs early in gestation it will lead to such extensive destruction that spontaneous abortion, mummification or still births may occur. If infection occurs late in gestation, or immediately after birth the cells that are most affected are in the central nervous system, and the retina, leading to unique clinical signs in young kittens.

Duration of Infection
When a cat is first infected with FPV, the virus will replicate for 4-7 days without producing any noticeable signs. Despite this, the virus usually enters the blood causing viremia within 24 hours of infection. Once the virus enters the blood, the body is stimulated to make antibodies against the virus. These neutralizing antibodies reach high titers and are effective at destroying the virus in the body. With proper supportive care (to learn more look here) clinical signs will usually resolve within 7 days after they begin. The cat can continue to shed virus for up to 6 weeks after signs resolve. After the virus has been eliminated, the cat will be left with high titer of antibody providing protection for many years.
Kittens which are born infected may also have an immunological tolerance, which would result in viral shedding for an extended period of time.