I want to travel to the airport in Schwechat, Vienna and I have a one-year "Jahrenskarte" to travel within Vienna. I am not sure if I can use this one to travel to airport as well or I should buy a ticket for that.
Just to be sure: I assume you have a year pass for "Kernzone Wien" without any other limitations, which gives you access to most buses, trams, subways etc. within vienna.
Sadly, the airport is the most notable exception: It is outside of the geographical area, and for some possibilites to get there even the inside part is excluded.
However, depending on your choice, the inside part might be valid, thus lowering your ticket price.
Other than private transportation and cabs, there are eg.:
The train line S7 as well as regional trains on the same route ("R" but not "CAT"), are trains with several intermediate stops, where the year pass helps.
Among the stops are: Floridsdorf (also subway U6 there), Handelskai, Traisengasse, Praterstern (U1,U2), WienMitte/Landstraße (U3,U4), Rennweg, St. Marx, Zentralfriedhof, Schwechat, and the airport.
Duration: From WienMitte eg. 24min.
Time between trains: Depending on the time up to 30min.
Price: Your year pass is valid up to Schwechat, the rest to the airport has to be paid. The ticket vending machines at any train stations allow you to change the departure station, just choose Schwechat there.
A single ticket without discounts (from Schwechat) should be 1.70€
From the main railway station (also U1 there) or Meidling (U6) , there is an ÖBB train without other stops, where the year pass helps too.
Interval 30min, duration: 15min from Hauptbahnhof / 30min from Meidling.
Price 1.70€ too for the outside part. Note that here you can't select Schwechat as departure because the train does not stop in Schwechat, however there should be a checkbox at the vending machine that you have a ticket for the Kerzone already.
The "city airport train" is a train from WienMitte/Landstraße to the airport without intermediate stops. Here the year pass does not help, and even then the price is pretty high.
Interval: 30min, Duration: 16min, price 12€.
There are also several bus lines, all of them are belong to the airport exceptions and are not included in your year pass. Eg.
Hauptbahnhof (U1) and Westbahnhof (U3,U6), every 30min, 8€
Schwedenplatz (U1,U4) and Westbahnhof (U3,U6), every 30min, 8€
Donauzentrum (U1), Kaisermühlen (U1), Donaumarina (U2) and some other stations, every hour, 8€
From Erdberg (U3 there), every 1-2 hours, 5€
Note that most of these stop service at some point in the evening. In the night, a cab might help more.
For german-speaking people, there is a nice overview on https://blog.wienerlinien.at/anreise-flughafen-wien/ which I also used as source for this post.