Mono, or mononucleosis, is spread through direct contact with saliva. This includes sharing eating utensils or drinks. Because it takes about 30 to 50 days for symptoms to appear, a person who's infected can spread the virus without even knowing it. Though no one really knows exactly how long it takes after infection with the virus for a person to become contagious, it's pretty safe to say that a person is most contagious from right before their symptoms start until they go away.
If you've shared drinks with or kissed someone who has mono, there's no way to tell whether you will get it — unless you know you've had mono before. People who have already been infected with the virus that causes mono — Epstein-Barr virus or EBV — will develop immunity that protects them from further infection. An estimated 95% of adults have been infected with EBV and 50% of children are infected before age 5. So you may very well have already had mono and not known it.
If you do get the symptoms of mono — such as fever, sore throat, and tiredness — contact your doctor to find out whether you need an appointment. If so, your doctor will examine you and may also do a blood test for mono. Other viruses and some bacterial infections — such as strep — may cause similar symptoms.