Florence, Italy to Interlaken, Switzerland
 

What is the least expensive and fastest route for this trip.

If you drive a frugal car shared by a few passengers, then driving would be cheapest per person. Otherwise, the normal way is the train, usually with changes in Milan and Spiez, sometimes also in Brig.
Flying is not an option if cost matters.

Train is much easier than driving, as the train route through Simplon and Lotschberg tunnels is shorter than any possible driving route.

I'm in the process of doing this very route as I write this but I am stopping off in Verrona.

take the train to Milan; change there for a train onward; as was mentioned you may have to change again in Brig and again in Spiez

Thanks...another question ...does the Swiss Pass activate in Spiez or Brig...and is it worth the cost for being in Switzerland for 7 days...leaving out of Zurich?

Add up the trip legs that you'll do within Switzerland then compare to the cost of the pass. If it's just from the Italian border to Interlaken and then to Zürich airport, I'm pretty sure a pass wouldn't be worth it, but maybe you have other trips in mind while based in interlaken? Check it out at www.rail.ch.

You would then buy an Italian ticket to the border station, maybe Domodossola or Chiasso where your Swiss Pass would kick in. But you need to read the fine print about activating the pass - it is usually a matter of going to a station and showing ID and having it activated. I don't know if that can be done on the moving train when the conductor comes by after the Swiss border.