At present, the only way to get to Sri Lanka is to fly into the island’s international airport: Bandaranaike International Airport (CMB). 

The journey from North America to Sri Lanka takes at least 20 hours, and necessitates at least one stopover.
From the east coast, the most direct routes go via Europe and the Middle East (direct flights from London, Dubai, Doha or Abu Dhabi).
Traveling from the west coast, the most direct routes go via East and Southeast Asia (direct flights from Beijing, Kuala Lumpur, Singapore, Bangkok or Tokyo).
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Flying to Sri Lanka from London takes about 10h30 with SriLankan Airlines on a direct flight. From other main European cities a stopover will be needed, usually in Middle East.
Flying to  Bandaranaike International Airport (CMB) from the Middle East takes about 4h30 with Emirates, Etihad and Qatar Airways. These companies fly direct from Dubai, Doha, Abu Dhabi or Riyadh.
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Sri Lanka is well connected with other countries in South and Southeast Asia. There are regular nonstop flights to various places in India, Thailand, Malaysia, China, Japan or Indonesia. 

SriLankan Airlines from London, Melbourne, Bangkok, Shanghai, Beijing: https://www.srilankan.com
Emirates from the USA: https://www.emirates.com/
Qatar Airways from Doha: https://www.qatarairways.com/
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