Well of course Symi is an island, so there’s always an element of ferry travel involved, but people can and do get here from Northern and Western Europe by car or rail. I covered this before in a now-lost post, but the information is updated to this week. For the rail options I cannot do better than refer you to that excellent website operated by The Man in Seat 61.
There were once several international rail routes into Greece, but now there are only a couple of trains a day, so the alternative is to travel by train to one of the Italian Adriatic ports, catch a ferry from there to the Greek ports of Patras or Igumenitsa, express bus to Piraeus, and ferry for the final leg.
For the road option, I acknowledge the help given by the trustees and volunteers of the charity Next Stop Symi, who make regular trips by van from the UK to Symi as part of their work in delivering aid supplies to refugees in Greece, and were on Symi in October 2017 collecting supplies from the depot on Symi for transfer to Rhodes and Athens.
Their preferred route again involves the Adriatic coast of Italy,which they find the quickest and easiest.While it is perfectly possible to drive through Bosnia/Serbia/Montenengro/Albania/FYROM on a variety of routes, as these countries are not EU members there can be customs and visa issues, there will certainly be border delays, and you need more expensive vehicle insurance.
Getting to the Adriatic coast does depend where you start from in Europe. All Alpine crossings are expensive to use, and both Austria and Switzerland require you to purchase and display a “vignette” showing you have paid local road taxes for your transit of each country.
Ports with frequent ferry links to Greece are: Venice; Ancona; Brindisi and Bari. It is a tradeoff between more time on the road and so more fuel used and road tolls incurred, and more time onboard ship and higher fares. The two main shipping lines are the ANEK/Superfast consortium and Minoan/Grimaldi, there are also some less reliable independents.
On the Greek side, some ferries use the port of Patras, some Igumenitsa, and some both. Igumenitsa offers a shorter sea crossing but a longer drive to get to your next stop (accompanied by more road tolls). You’re aiming for Piraeus, the port of Athens, which has daily sailings by Blue Star to Kos and Rhodes, two or sometimes three a week of which call at Symi on the way.
Next Stop Symi offer two final invaluable tips: Always keep the ferry ticket stubs for your crossing from Italy. If you bring a motor vehicle into Greece for over 6 months, you must re-register it in Greece and pay import duty. The ticket stubs are your only proof of when your vehicle arrived, without them it may be impounded.
Oh, and have a teddy bear on board with you. The sight seems to make tollbooth operators and customs officers stop being officious and start laughing.