Note that there are examples of scoring in the computer simulation of the game.
There are many ways of scoring but here is the one that I use.
When someone has gone out, the scores are added up (the banker's being doubled) and the score of the winning hand is awarded to the winner by each player, (the donation by the banker being double if the banker did not go out).
When calculating the score, all of the points are added up and the number of doublings is added up. The score is then doubled this number of times.
To go out (finish the game), a player needs to have 4x3s or 4s of a kind plus a pair. You may substitute runs for the threes and fours of a kind and if you pick up the last tile of the run from the discarded tiles, you must declare it in the same way as you would declare a three or four of a kind.
Usually, a limit to the score is set and if that limit is exceeded in a game then the limit is used as the score thus, people are protected from a single, high-scoring game which could upset the whole score. In this way, the dynamics of the game can be modified. With a low limit, the players' performances over the whole set of games is taken into account whereas with a high limit, only the most recent games influence the score.