Ticket to Ride: First Journey takes the gameplay of the Ticket to Ride series and scales it down for a younger audience.
In general, players collect train cards, claim routes on the map, and try to connect the cities shown on their tickets. In more detail, the game board shows a map of Europe with certain cities being connect by colored paths. Each player starts with four colored train cards in hand and two tickets; each ticket shows two cities, and you're trying to connect those two cities with a contiguous path of your trains in order to complete the ticket.
Don't just take our word for it! Check out this review of Ticket To Ride - First Journey Europe.