The aim of On the Underground is to gain points by building lines, and having the Passenger use your lines. Each player takes control of several lines, and on their turn does the following:
Build Track: Each turn a player builds four lengths of track on the board. The first length of any line can be built anywhere, but later lengths must extend the existing line from one of its ends. You may branch your track by paying branch tokens, which you collect by skipping track builds and by building to termini. You get points by building track to National Rail stations or termini, by linking connection stations or by building loops.
Move the Passenger: Then each player moves the Passenger to one or two destination stations. The Passenger is lazy, and chooses his route to minimise the distance that he has to walk, and the number of lines he has to use. For each line that he uses, the owner of that line gains a point. The visited destination cards are replaced, and it is the next player's turn.
When the deck of destination cards has been exhausted, the game ends, and the player who has gathered most points wins.
For further details about how to play, you can download the rules, or look at the frequently asked questions page.