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.
Details for Bus 250:
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.(Aug.-Oct 2018, bus 250 does not stop at Jakominiplatz,
but at Schlögelgasse, off Dietrichsteinplatz. That's 200m from
Jakominiplatz, via Reitschulgasse.)
From Graz train station, take bus 58 to Mariagrün and change to bus 250 at Kroisbach-Postamt (on Mariatroster Strasse across the street from "Diagnostikzentrum"). This connection may be faster than going by tram via the center of Graz.
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 St. Leonhard/LKH), 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.
(Note: Aug. - Oct 2018, you need to change at Dietrichsteinplatz, instead of Jakominiplatz. - Take streetcar 3 or 6 only and get off one stop after Jakominiplatz, at Dietrichsteinplatz.) 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).
A single ride Graz - St. Radegund is Euro 6.40. Also, you can get a
"10 zone" ticket (at the train station and at most tobacconists in Graz)
for Euro 19.80. For a single ride Graz - St. Radegund
you need to punch 3 zones, worth Euro 5.94.
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 for Euro 24.70 at a ticket counter at the train station, in the central ticket shop "mobil zentral" Jakominigasse 1 (just off Jakominiplatz) and also from the driver of bus 250. (Prices as of July 2015).
Directions to Yeshe Sal Ling (once you have arrived in St. Radegund) here<