|You'll get a lot of points going for the "Rummy Master" achievement, so just build on that, and remember that any points accumulated count, be it single player or online. You have to finish a match completely for the points to count, but it doesn't matter whether you win or lose.|
To see your current total, from the main menu go to Help & Options -> Player Statistics.
The easiest way to rack up points is by boosting online. With a buddy, if you play Classic Gin, and one player scores no points at all, then the other will get a bonus in excess of 300 points from quite minimal work. Also, you can help each other get gin bonuses and the like pretty quickly.