Fastest transportation from Geneva to Salzburg

The quickest way is probably fly to Munich, then train to Salzburg. Geneva to Munich is flown by Lufthansa and Easyjet.
Salzburg has a small airport, but no flights to there from Geneva.
The alternative route is train, Geneva to Zürich than Zürich to Salzburg. This would take 8h40, with one train every 2 hours. For example:

Genève dep 09:42 4 IC 1 715, Zürich HB arr 12:28
Zürich HB dep 12:40 9 RJ 167 Railjet, Salzburg Hbf arr 18:21

Not sure why you are mentioning Hallstatt, you said Salzburg in the first sentence. Going to Hallstatt, you do not necessarily go via Salzburg.

Assuming your goal is actually Hallstatt:

That's an extremely long trip, requiring you to traverse all of Switzerland and about half of Austria lengthwise. Rome2Rio suggests it is going to be quite a challenge. The best train connection (verified on the Deutsche Bahn website) seems to be a 7:42 AM departure that gets you to Hallstatt at 6:47 PM after three changes. Later departures make for an overnight trip.

Somewhat faster options include rental car (brace for the international drop charge) and flying (quite likely with connecting flights) into Linz, Salzburg or (probably non-stop) Munich and taking the train from there.

Switzerland has gorgeous lakes of its own; I'd seriously consider skipping Hallstatt, given what that travel day is going to look like.

Thank you. I wasn't clear about Hallstatt. We have decided to fly from Geneva - Salzburg changing planes in Frankfurt. One in Salzburg we will take the train to the Ferry that takes us to Hallstatt where we have accommodations. We will head back to Salzburg for 2 days then on to Prague.
Thank you again,
Carrie

We have decided to fly from Geneva - Salzburg changing planes in Frankfurt.

Depending on how long you will be at Frankfurt airport, it is almost certain to be quicker (and definitely easier) to just fly direct to Munich and take a train from there to Hallstatt. There is a station at Munich airport.