Whenever you would place a scoring marker on a station space (either as a result of excavating the last rubble on a rubble space, or by building a building) then instead of doing so you may choose to take any one other player's scoring marker and place that on the space instead.
If you do that then you immediately place one or two of your own scoring markers on that player's Share Portfolio (a card, as indicated in the picture) - if the pint value of the space which you gave them was from 1 to 9 (inclusive) then place one of your scoring markers, and if it was 10 or more then place one OR two scoring markers (it's your choice).
You now have shares in that player's points - you can have as many shares in other players as you wish, but cannot have shares in yourself.
When the normal scoring has been calculated at the game's end, for each player in whom you have a share you gain 1 point for every 10 points of their final score for each share that you have in them. Add those points to your total score.
This mini addition was initially released on Boardgamegeek. It was subsequently formally printed with Dick Train on the reverse and given to purchasers of North American Railways (and those who asked Tony nicely) at the 2018 UKGE.
It is for use when playing with 3 - 5 players only (the more players, the more share spaces are in use). A high-resolution for print-and-play usage may be found here.