Travel from Stuttgart to Luzern to Zermatt and back to Stuttgart in June?

Hi, I'm a budget traveller who is interested in travelling from from Stuttgart, Germany to visit Luzern and Zermatt in Switzerland. I only have a week to travel to these two places in June. Is there any advice on the cheapest transport I can take and travel tips as well?

Oh, and would anyone be able to provide me information on these two places? Any information which would benefit a new traveller. =)

Thanks a million!

from stuttgart from you come with train to everybody city also luzern:) is believe also the cheapest one.

Here you can check the trains:
There are cheap train tickets from Stuttgart to Luzern for 19€!
http://www.bahn.de/international/view/en/index.shtml
http://reiseauskunft.bahn.de/bin/query.exe/dn?ld=212.199&seqnr=2&ident=aa.023214199.120758188 1&rt=1&OK#focus
It's better when you book the tickets as soon as possible coz the cheap ticket are sold out early.
http://www.luzern.org/en/welcome.cfm?
http://www.zermatt.ch/index.e.html