Is kissing (getting thier saliva) a person with mononucleosis the only way to get the disease ?

Not the only way: Infectious mononucleosis ("mono") has been called "the kissing disease" in popular culture for years. It is caused by the Epstein-Barr virus and is mildly contagious. A person gets the virus from direct contact with an infected person's saliva, through activities such as kissing, sharing food, sharing drinks, getting sneezed upon, etc...

Sort of: Epstein bar virus, which causes mono is spread from saliva but kissing is hardly the only way to share saliva, though kissing may be the way to share that is the most fun. Sharing food, glasses, silverware, etc are all ways to share saliva and as such to spread the virus.

Not just kissing...: Epstein Barr virus EBV), the virus causing mononucleosis, is spread primarily through saliva, but can, in rare cases, spread through blood (e.g. infected organ or blood donor). The important point is that a great majority of people ( up to 95% in some studies in the US) have mono and can shed virus intermittently even when asymptomatic, making it almost impossible to avoid infection.