Swiss Half Fare Card

Booking in advance does not give any advantage unless you are trying to get Supersaver tickets, which can only be booked on-line within 30 days of your travel date and you must use the exact itinerary shown on the ticket. That can get you up to 50% off and then you get 50% off of that with the Half Fare Card. But almost all trains in Switzerland are unreserved and always the same price.

So if you buy at a ticket counter, just show your Half Fare Card. Buy out of a ticket machine, and just push the button that you have a Half Fare Card. Buy with your smart phone, click that you have a Half Fare Card. The key is when the conductor asks to see your ticket, you must show your valid Half Fare Card so he/she knows you paid the right fare. If you don't have it, you have an invalid ticket and then the trouble starts.

You don't even need to have a Half Fare Card when you buy the ticket, but you better have it before you board the train.

As far as getting a connecting ticket from Spiez to Muerren, yes get it now so you don't have to waste time buying one at the station in Spiez, where it might be a tight connection. You'll miss a train in the time it takes to buy a ticket, although you can just wait for the next train since you can take any train on that route for that day. Swiss policy is to have at least one train per hour in each direction at every station in the country.

Unless it's a special train, think of the trains here like a subway- you purchase a ticket and get on the train. If you will have Internet, download the sbb.ch train app. Once you have your half price card, add it to your account. It's very easy to buy a ticket as you need it on the app and you won't have to show 1/2 price card when you show your electronic ticket as it's already there. Keep your 1/2 price card with you in the event you just buy a paper ticket and need to show it. Ticket machines and the app offer multiple languages so easy to switch to English. You will see where to select 1/2 price ticket easily.

Great, thank you for this feedback! Do you think I should still buy my Half Fare card before my trip? Or would you suggest buying it when you arrive in Spiez?

If you are travelling by train from Venice to Mürren, your half fare ticket is valid from the Swiss border.
So you can buy an Italian ticket from Venice to Domodossola (the border station), and a Swiss half price ticket from Domodossola to Mürren. This may (or may n ot) be cheaper than one ticket Venice to Spiez, and a half price ticket Spiez to Mürren.

This is all shown on the map that comes with the half price card, copy here: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich_en.pdf

The only advantage in buying your half fare card in advance is saving time at the station. It does not matter that you don't get off the train at Domodossola, as long as you already have a half price card and ticket at that time.

Using a ticket machine is quicker than waiting at the manned ticket desk. The machines have two options, full price or half price / child.