You get 12 CP for winning the target, when someone takes that from another clan, they get 11, then next time 10 and so on. There might be more points for DOM and TDM, as you need more wins to get those targets.
They also updated so you get CP for holding the targets for I think it is 24 hours, don't know how many points though.
(also, depending on how big the clans in your division is, there may be less or more wins needed to capture a target. There are only 3 in each clan in our division, so we needed 5 wins in Cranked and Kill Confirmed to take that target, we already have 24CP and are the only ones in our division who have played).