Upvote:2
You can get from Munich to Thierhaupten by a combination of train and bus. Visit bahn.de for detailed information. Selecting "München Hbf" as the starting point and "Marktplatz, Thierhaupten" as the destination gives prices between €20 and €30, depending on the trains involved.
If you want to hitch a ride in a car there is a ride sharing site called Mitfahrzentrale, without a guarantee that you find something which matches your needs.
Upvote:3
Eurolines sells tickets from Munich to Augsburg for 5 Eur (apparently only one bus leaving at 17:30). These are far distance coaches, so check with the company for possible delays before you book.
From Augsburg to Thierhaupten with the Augsburger Verkehrsverbund costs 9 Eur. For connections, see also lines 410 and 410/413 on the web page of Thierhaupten.
Possible itinerary for April 4, 2019, cheap but not easy:
Eurolines
17:30 Munich, central coach station
18:30 Augsburg, Biberbachstrasse 9
walk, 6 min
(Unfortunately, you've just missed the last bus 410 from Oberhausen, Nord P+R to Meitingen/Thierhaupten at 18:24.)
Tram/Straßenbahn 4 > Augsburg, Hbf
19:37 Oberhausen, Nord P+R
19:45 Augsburg, Wertachbrücke (*)
Tram/Straßenbahn 2 > Augsburg, West P+R
19:48 Augsburg, Wertachbrücke
19:50 Oberhausen Bf/Helmut-Haller-Platz
Regional train/Regionalbahn R4 > Donauwörth, Bahnhof
19:57 Augsburg Oberhausen Bf/Helmut-Haller-Platz
20:13 Meitingen, Bahnhof
Bus/Regionalbus 410/413
20:20 Meitingen, Bahnhof
20:33 Thierhaupten, Marktplatz
(*) This is the suggested route by the Augsburger Verkehrsverbund. If you are early, you could also continue to Augsburg Hbf instead and take the R4 train from there.