You start the game with 5 houses around your train station and need to earn money to upgrade your trains, houses or buy new houses. To do so you need trains and passengers.
Passengers are generated by the various buildings and they spend a fixed fee (depending on building and people genereated in that building) when getting on the train. In order to get people on the train, you need to click on the building, if it shows that there are people waiting in it, in order to send them to the train station where they wait for the next train.
You can get 10 own trains in total. The basic trains are free when starting a new route.
To create a new route you just need to select one of your facebook friends which generates a 1 stop route of 100 miles. Depending on the train used it will take a some time to get back to you to pick up new passengers and generate more income. The more stops there are on a route the more you will earn but the train will also take longer to get back as each stop added adds 100 miles to the route.
So send out your first 10 trains and try to select friends who will accept the invitation. If an invitation for a train is accepted you can add a new stop to that route by inviting another friend. If an invitation is accepted the stop/friend is permanently added to that route and cannot be removed or moved to another place of that route (a friend on 1st stop will always remain the 1st stop of that route) except by deleting the route completely. As long a the request has not been accepted the request / friend can be removed from the route.
Tips to get things going faster:
You can send all your trains to all your friends that play Lucky Train, there is no restriction that you could only send 1 train to any friend: send all your trains to the same friend and ask him to do the same with his trains. This will bring more trains to your and his station and generate even more income, doing so with all your Facebook friends will bring lots of coins which is only slowed down by the invitation limit of Facebook.
If a friend does not answer the invitation after 1 or 2 days, just remove him from the route and try another friend, else you'll get stuck with low income per train.
Add more stops to routes by adding friends whenever possible. The more stops the more bonus cash and experience you will get for every stop and passenger on that route.
Try to load your most valuable passengers to trains with most stops for the bonus experience and cash you get per stop.
Upgrade your trains as they will run faster and / or can carry more passengers, so that they get back faster to your station. This bonus is based on number of stops, passengers and the fee they pay.
Upgrade your houses (whenever possible) and buy new ones in order to get better paying and more passengers.
Experience is needed to gain levels which unlock new buildings.