This will keep track of how many you have earned in total, you don't have to have 10,000 in one instance. Other than playing normally, going on quests, doing rushes, sending people out, etc., I find that finding and clicking on the mysterious stranger helps a lot.
Occasionally you will here a *Dun dun dun* sound occur randomly, which signifies that he has appeared in one of your rooms. He wears a hat and a long coat and only appears for a short time. If you find the room he is in and click him, he will reward you between 100-1500 caps. In a single hour of playing, I managed to net around 3000 caps from him alone. Although purely luck based, some pets will also increase the chances of him appearing.