Ticket to Ride played in the usual fashion, however when it comes to having the right number of cards to claim a route, you have to roll a die of the same number in order to claim it. This means you can only claim a route that is the same length as the number on the die. Just like in C & L, you can only move the number on the dice.
The die would be a normal six-sided die. Since there are only routes of 2 to 6 in length in TTR, if you roll a 1 on your throw, you will lose your turn.