There are several airlines that fly into Salzburg all year round.
Salzburg Airport helpfully publish a full flight schedule to help you find a flight that suits you best.
The hire of a rental car is recommended although not essential. The drive from Salzburg Airport to St. Gilgen is around 25 minutes, via the A1 autobahn to Vienna, taking the Thalgau exit and then continuing through Hof and Fuschl.
There are trams running from outside the airport terminal to central Salzburg bus station (20 mins) then take the 150 bus direct to St Gilgen (50 mins).
Flights in and out of Munich are readily available on a wide variety of airlines. From Manchester, Lufthansa and Easyjet fly year round. Similar services from the rest of the country to Munich make this very accessible. A slightly longer drive, but more scenic is from Vienna, about 3 hours driving and year round flights from most capitals.
Vienna also boasts a direct rail link from the airport to Salzburg which is very cheap and only takes 2h45min. This is the Railjet Service and can be booked via DB or TrainlineEurope.
Car hire is also cheap in Germany. Travel time to Salzburg from Munich is about 1.5 hours and is a simple trip along the autobahn making this a very viable way to arrive or depart. Munich can also be easily reached by rail and is very cheap. Travel is available either on DeutscheBahn or OBB.
If you want to bring your own car and drive the whole distance, travelling time from Rotterdam is approximately 11 hours. P&O Ferries provide an overnight service from Hull to Rotterdam with excellent facilities and amenities onboard. Other services are also available, but the benefit of travelling through Holland and Germany is that you avoid the French toll roads.