Finding CCS members: Get someone with good disguise skill to show up at the Cigar Bar (you know, the place where they only let you in if you look rich/like a security guard. When inside, find a hick, rube, or similar. These people are 99% of the time members of the CCS. If your infiltrator is persuasive enough, you can actually get them to attend a meeting and turn them the way you turn liberals. If not, you need to torture them for information by using someone talented for that.
Raiding the CCS: When you've got someone on the "inside" of the CCS, you can go to the lair the person is at, and raid it by killing numerous members (I'm not sure what the limit is at these days, but I think I once raided a place, killed ten people, and got it Liberal). Keep in mind they are heavily armed and have good armor, so come prepared with the best guys you can get.
After around 4 of these raids (on different locations), you'll have defeated the CCS. I find the CCS to be ludicrously simple to defeat due to my playstyle, but I guess that's just me.
If you need advice on getting people talented at killing people without getting a lot of heat: Train someone to the point where they can recruit Agents. They are decidedly the most bad-ass recruitables ingame, and are well-suited for raiding a location
If you need money; I suggest using your main man with a charismatic group to infiltrate the court house repeatedly, and gain enough Juice to up them a lot. When they can all recruit 5-6 people, have them recruit basically anyone, and have them perform either legal or illegal fundraising (to be honest, they both end up with jailtime, so I don't see the point in calling one of them illegal...). When you have 25 people selling brownies for you, you'd be amazed how fast you can earn cash.
It's unwise to have your Main Man's underlings do a lot of crime, as it leads to them getting imprisoned if they don't have really high law skill, or you feel like shelling out 5k a piece for their freedom. Another good piece of advice is recruiting judges etc for your squad, as they already have high law skill, and you'll spend less money training them.
My main man had at some point 18 in Law and 21 in Persuasion. My entire group was comprised of Agents. I wiped out the CCS in less than a month with no casualties.