My approach and experiences
When we arrived we went door to door with the whole family to introduce ourselves. We offered a little gift from Holland (cheese, cookies), which really helped because we didn’t speak German. Giving a little gift doesn’t need many (German) words, neither does saying your name or the country you are coming from.
Teach yourself (maybe with some help) some basic, but important German sentences (like ‘Hello’/good morning/good afternoon/good evening’, ‘Excuse me’, ‘Have a nice day’, ‘How are you doing?’, ‘I am sorry, I just speak a bit German’) and practice them! Even if you don’t have a clue what they say back to you, that’s ok. I don’t think most Swiss expect ‘foreigners’ to be fluent in German. Just trying already means a lot to them and it’s so much nicer than starting immediately with “Do you speak English?”
I ask for help and information. If I receive post I don’t understand or I am looking for a specific type of shop or a nice restaurant, I ask my neighbours. I also ask them about local festivals and customs. Of course Google translates well and the web is available and easy, but asking the people around you who have lived here for years is much more fun than sitting at your computer or tablet.