The closest large airport to Füssen is Augsburg Airport, 110km away. You can catch a shuttle bus to the train station and make a connection to Füssen. The smaller Memmingen Airport requires a taxi to the Main Station, then train connections to Füssen via Augsburg.
The most popular airport connecting to Füssen is Munich Airport, where you can take an S-Bahn Train to the rail station and head for Füssen on the train.
There are many connections to Füssen from Munich and vice versa. Direct trains leave about every two hours. Other options require a change of trains along the way in another city. The cheapest ticket for this trip (especially if you are travelling with others and if you are going to return on the same day) is called “Bayern-Ticket” which is 22€ with every additional person up to a maximum of five only 4€. It is valid in all RE, RB and ALX trains on this track, but not in the ICE!
In addition make sure you start your trip not before 9 am as the ticket is not valid before except on saturdays and sundays.