Train Prague to Salzburg

Check Deutsche Bahn website. Some are expresses some are not. You have to change trains at least once.

The fastest connections I find on the German Rail website is Prague to Ceske Budejovice to Linz to Salzburg in 6½ hrs. But that connection is entirely outside of Germany, and you can't get a fare from German Rail. Probably the least expensive (an hour longer} uses the express bus from Prague to Nürnberg, an ICE to Munich, and another express train to Salzburg. That route is €29 pP with advance purchase.

I did this trip, in reverse, the summer before last. It's a long, full day haul. Even first class some of the Czech trains are pretty minimal. After the first leg (going south) you have a really brief transfer, but they know you are coming and the train waits. The next transfer doesn't even have a station with a platform. You hop off down to the gravel, walk over to the next train, and make the big step up. Take food and water, you can't get any along the way. The toilets on the second train are worth a photo (I took one). A fun note: on the transfer without a platform, I asked a workman (the only person around to ask) "Praha?" to which he said "Ano" (emphasis on the no, sound like the no in English). I asked several times and was getting worried whether to get on the only train in this tiny place. Later, I found that ano means yes in Czech.
BTW, there is a special pass on Czech rail that lets you go to Prague and out (not amble around) at a good rate. You can get it in advance and avoid having to buy the ticket on the train, with a possible fine.

Dennis, Really absolutely no drinks for purchase? Also, you mentioned two transfers...does the train wait for you at both? Do I need to understand Czech to make sure I'm on the right train each time? Thanks! P.S. curious about the toilet.....

On the stretch from Salzburg to Linz there was food and drink. Once we hit Czech trains (on this route) there was none - we walked the entire length of the train. Hopefully they have added some in the two intervening years. The trains wait for you as they know when the other trains should arrive, and they run on schedule. Indeed, if they didn't wait there wouldn't be many passengers on board, as there were only several dozen of us of us as it was. No need to know Czech, as I have suffered the panic for you (he probably thought "what part of ano doesn't this dimwit understand???). The Czechs are wonderful, as are just about everyone we have ever met in almost 40 years in Europe almost every summer. Our French, Spanish and German are quite passable, but Czech is a mystery to me.