Train travel

First, I will add the standard caveat that it is not a good idea to book reserved tickets (i.e. ones only valid on one specific train) after a long flight. Planes can get delayed by hours.
To answer your question, go to www.sbb.ch (Swiss Railways website) and enter Zürich Flughafen to Lech, and date and time. looks like Lech does not have a station, the last leg will be a bus. It gives you a choice of bus stops, for example "Lech Postamt" (the post office).
P.S. if you want English, click on the small 'en' top left.

Looks like it takes about 4 hours. You can then get a price. For a random day in March it is offering CHF 56 for an open ticket (valid on any train) of CHF 28 for a ticket on a specific train.

For tickets wholely within Switzerland (Wengen to Zürich) there is no discount for advance purchase, all tickets are the same price and valid on any train. So for this trip just buy tickets at the station on the day (or the day before, but be sure to ask for tickets for "tomorrow" in this case).

Go to http://www.sbb.ch/en/home.html

Put in Zurich airport, St Anton am Arlberg, and your date of travel and you will see your options.
Looks like full fare is 59 CHF per person, but there is a nonrefundable, nonchangeable ticket offered for 29 CHF. If you miss your train, that ticket becomes worthless. I've done this, leaving about 4 hours from flight arrival and train departure and I lucked out. You can take an earlier train to Zurich Hbf, store your luggage in a locker and nose around Zurich until the your train to St Anton departs. At St Anton, get a bus to Lech.
You can also get something off the train to Wengen, since the St Anton-Zurich leg is subject to discounts.
Wengen to Zurich airport might also have a nonrefundable discount by clicking the "Supersaver" button when you go through the ticket purchase process.

PS delete your other identical thread.

Here is the bus schedule from St Anton Bahnhof to Lech.
http://www.stantonamarlberg.com/media/819/download/Linie%2092_ab13.12.2015.pdf?v=1&inline=1