There are two ways to get to Methana one is by road and the other is by ferry.
By road from the airport to Methana is 195 km and about two a half hours to three hours is the duration of the journey.
You can rent a car from the airport or take a taxi to get to Methana. www.dritsastaxi.gr
There is also a long-distance bus KTEL from Athens to Methana. If it is a large group we can arrange small minibus to come and pick you up from the airport.
Map here: https://www.google.gr/maps/dir/%CE%91%CE%B8%CE%AE%CE%BD%CE%B1/%CE%9C%CE%AD%CE%B8%CE%B1%CE%BD%CE%B1/@37.8812738,23.2598459,9z/data=!4m8!4m7!1m2!1m1!1s0x14a1bd1f067043f1:0x2736354576668ddd!1m2!1m1!1s0x149f7fffd4b6c483:0x2ffd9611425b04fc!3e0

The best way of course is to take the metro from airport to Piraeus is about 55 minutes.
From Piraeus there are ferries to Methana daily at 9:00 am, in the summer season (June to September) the cost is 15 euro. There are 4 flying dolphins every day and it takes about 1 hour from Piraeus to Poros island that is very close to Methana, only you have to take the ferry to go to the other side Galatas is about 5 minutes, and from Galatas to  Methana is 21 km. The cost is 32 euro for flying dolphin.
https://www.ferryscanner.com/el/ferry/results#search/dep/PIR,POR/arr/POR,PIR/date/2022-10-08,2022-10-13/passengers/1/vehicles/0
There is also a regular ferry , but only one in the day the summer months.
https://www.sf.gr/ell/