How can I change the language of the GUI of Mathcad?
That depends on the version you are using:
For full-grown Mathcad (15 and below) you go to menu, "Tools"/"Preferences..."/Tab "Language"/ and here you can set the menus and dialogs as well as the Math language from German to English. I recommend doing both and while you are at it you may also change the spellcheck language to English. The change will automatically affect the built-in help, too, and switch it to English.You will have to do this only once and the changes take effect on the next launch of Mathcad.
If you are just using Prime its much less user friendly (but then thats the case with most things in Prime). The Math language is English in all versions, which I consider a good thing. I didn't like to see "solve" in one sheet and "auflösen" in the next. To get the GUI in English you have to use the commandline switch "/culture:en-US" w/o the quotes. You may edit the preferences of the desktop icon and add that switch. Nevertheless if you double click a mcdx-file it will still open with the German GUI. You will have to fiddle around in the Windows options to add the commandline switch at the appropriate place or directly change the open command for the mcdx extension in the registry. Also the Prime help will still be in German, but at least, beginning with Prime3, you can change the help language permanently: fire up help by pressing F1 in Prime, chose the configuration tab (its not labelled, its the one with the yellow star) and then the second icon which looks like ..no clue!? This setting, if saved, stays in effect from now on, no matter if you start Prime in German or English.