I just returned from three weeks in Switzerland, and my trip was much improved by the advice and suggestions I got here; thank you for all the collective wisdom you have shared!
If you're going to be in Switzerland for a while, moving from place to place, and will have internet access, the SBB app is well worth downloading before you leave home. I bought my Half Fare Card at the Zurich airport train station, and after that I was able to purchase all my tickets using the app, sometimes while standing on the platform waiting for the train. I set up my information so it knew my credit card number, which made purchasing easy.
The app keeps track of your purchased tickets, and you also get an email for each purchase. You just show the electronic ticket (which has a QR code) to the conductor, who scans it with his/her phone. It also provides schedule information, just like the website does. You can't use it to buy travel passes, but that's the only thing I found that it couldn't do.