Feline Leukemia is actually a virus rather than cancer. The condition was misnamed due to early cases sharing symptoms in common with leukemia. By the time the cause was identified as viral in nature, the name had already found itself into so much literature and vocabulary that it stuck.
FeLV - often called Feleuk (fee-look) by veterinarians can be spread between cats via nasal or oral secretions. Sharing common food and water bowls is one method by which the virus often transfers between cats. Biting, nursing and sharing a litter box are other methods of transmission. A common description of the virus that is readily understood by laypeople is Feline AIDS, as the primary cause of fatality with FeLV is the same - compromised immunity.
There is no evidence to imply that Feline Leukemia is transferable to humans, dogs or other non-feline pets. In fact, overwhelming evidence implies the contrary as there has never been a case of FeLV detected in humans or dogs which are often exposed to infected cats.
Approximately 40% of infected cats manage to defeat the virus entirely. Others progress through multiple stages (in some cases defeating the virus). 30% of animals unable to defeat the virus experience a full progression which is usually fatal. The virus itself does not kill the cat; it compromises the animal’s immune system generally leading to fatality caused by any number of infections the weakened immune system is unable to stave off.
As of this writing there is no cure for feline leukemia though treatment aids are available. That said, your best course of action is one of prevention. Vaccinations against FeLV are readily available. Consult your vet to schedule vaccination and ensure he fully briefs you on potential complications arising from vaccination.
For more on cat and dog health and symptoms read our post How do I know if my dog or cat is sick