First, how to get to Graz: There is a direct train
from Vienna to Graz every hour. Also, there is a good connection by
train from Vienna airport every hour, and a direct train from Vienna
airport to Graz about once every two hours.
There are 6 direct trains per day from Praha (via Brno) to Graz,
and also several direct trains Munich-Graz.
The duration of the trip Vienna-Graz is 2h 30min, Vienna airport - Graz
3h, Brno-Graz 4 hours, Praha-Graz 7 hours, Munich-Graz 6 hours.
Look up train schedules on OeBB website.
For connections from Vienna airport, enter "Flughafen Wien" to Graz.
Graz also has an airport, Graz Thalerhof (GRZ) that is served by Austrian, Lufthansa, KLM, BMI, Turkish Airlines, and Swiss. There are direct flights to Graz from Amsterdam, Birmingham, Düsseldorf, Frankfurt, Istanbul, Munich, Stuttgart, Zurich, and Vienna.
From Graz airport, take the airport bus to Graz Jakominiplatz and (keeping the ticket, which is valid for part of the continuation of the trip) change at Jakominiplatz to bus 250.
From Graz train station, take bus 58 to Mariagrün and change to bus 250 at Feuerwache Kroisbach (on Mariatroster Strasse across the street from "Diagnostikzentrum" and "Spar". This connection is usually faster than going by tram via the center of Graz to Jakominiplatz.
From Graz train station, alternatively, if you want
to go to St. Radegund via the center of Graz, take any of the streetcars
departing from platform A in the subterranean streetcar
station in front of the train station:
1 (to Mariatrost), 3 (to Krenngasse), 6 (to St. Peter) or
7 (to St. Leonhard/LKH). Keeping the ticket, which is valid for
part of the continuation of your trip,
change to bus 250 at Jakominiplatz.
Or, if you take streetcar 1, you can continue past
Jakominiplatz and change
at "Hilmteich"; in the case of a tight connection, you might still
catch a bus at Hilmteich that you would have missed at Jakominiplatz.
Also, in case you miss the bus, the Hilmteich area is a pleasant place
to wait; there is a park and a pond (the eponymous Hilmteich).
Tickets: A single ride Graz - St. Radegund is (as of May 2025) Euro 8.50. Also, you can get a slightly discounted "10 zone" ticket (at the train station and at most tobacconists in Graz). For a single ride Graz - St. Radegund you need to punch 3 zones. You can get a weekly pass (valid seven days from the time of purchase) for public transportation inside Graz (including Graz airport) and between Graz and St. Radegund at a ticket counter at the train station, at the central ticket agent "mobil zentral" Jakominigasse 1 (just off Jakominiplatz) and also from the driver of bus 250.