For people with tickets for the games trains as well as local transport from 00.01 of the game day until 12.00 of the following day is free.

There will also be an option for people without, but the prices will be released on 01.03.08 only.

For the first time at an event of this size, access to cross-border public transport is included in the match ticket. If you have purchased a match ticket, travel to and from a match in Switzerland and/or Austria is included. You will travel comfortably and without stress by train, bus and tram on the day of the match and back home again up to 12.00CET the following day, free of charge.

For fans without a ticket here is the deal:

The UEFA EURO 2008 Half-Fare Card allows you to travel at half the normal fare in the whole month of June 2008 on the entire Swiss and Austrian rail network.

Advance sales until June: CHF 39.–
From 1 June: CHF 59.–

Or:

With the UEFA EURO 2008 Swiss Card, guests from abroad will be able to travel in June 2008 from the Swiss border or a Swiss airport to one of the four Host Cities and back again. The UEFA EURO 2008 Swiss Card also entitles you to a 50% discount on other travel by rail.

Prices.
* 2nd class: CHF 116.–
* 1st class: CHF 147.–

NOTE:

The Card's validity lapses as soon as you have used the transfer back from the Host City to the border or airport.

The Card is valid only for the direct route from the Swiss border or a Swiss airport to a Host City and back again. The transfer does not include travel by local municipal transport

How does it look with the name written on ticket? If I'm not that person and this person is not travelling with me?

same for me.. but I think & I hope they will not check names on tickets.. just a waste of time for them

think so, too, and you can as always say you are not the main applicant.