Ah, that's a good question. I wondered about that for awhile too. 

The easiest way is with CvC. Collecting the high end rewards SHOULD give you clan points even if your clan is at level 1. You can also collect clan points during a CvC with personal rewards as long as your clan wins. You also get clan points for 1st, 2nd, and 3rd place for Hydra and Chimera from your reward chest. (Also, you should get come points for seige too I think). Outside of these events, I don't think there is any personal things like arena, clan boss or dungeons you can do to earn clan points.

In short, if you are in a clan for awhile and not getting any points, then I might look to move to a better clan. If your clan isn't getting the last 2 rewards in CvC, then they aren't trying. But, if you're new to the clan and don't have any yet, give it a month or two and see how it feels there.