While Symi Island does not have its own airport, visitors can fly into nearby Rhodes. Multiple airlines operate direct flights to Rhodes from all over Europe. Otherwise, you can fly to Athens first and connect to Rhodes from there.
There are three different companies (Blue Star Ferries, Dodekamisos Seaways, and Anes) operating ferries from Rhodes to Symi multiple times a week. The journey is approximately 50 minutes. There are plenty of activities and accommodation options on Symi Island.