Assuming you have an option to switch ISPs (and I realize that many of you don't), it's actually pretty easy to do, even with leaving Comcast. This is really just an order of operations issue. Most people will decide they want to switch, call up their incumbent ISP to cancel their service, and then order their new service. Seems logical, but for best results, flip it around. Once you have decided to switch to the other guy, call the other guy first. The other guy will then set up your account, come to your house and do all of the installation, port your phone number over (if applicable) and then once you have verified that the service is working to your satisfaction, you call up the incumbent and tell them to cancel. This is how I switched from Comcast to Verizon a few years ago. Granted, I still dealt with an extremely defensive (anti)cancellation person on the phone, but it was a much more straightforward conversation. It went something like this...
Me: Hi. I switched to Verizon, cancel my service
Comcast: Why do you want to cancel?
Me: Your service doesn't work, I've had a tech out here 3 times and they didn't fix the issue. Fios has already been ordered and installed and it is working, which is something I could never have said for you.
Comcast: defensive statement...yada yada..Verizon installed a new wire to your house, that's why it's fixed
Me: Yeah, maybe you should have tried that on one of your 3 service calls, but you didn't. Anyway. I 'm not going to argue with you. I'm already receiving Verizon services, Comacast services have been physically disconnected. Cancel my account.
Comcast: Fine. Done.
And that was it. Hell I could have kept it even briefer if I had been prepared for such a defensive attitude, but even still, since you have physically disconnected their service and are already paying for their competitor, you know they have a snowball's chance in hell of getting you to agree to sending another tech over to re-connect Comcast and then go and cancel Verizon.
Now if you are not planning on switching, but want to pay less, or want better service, I use their anti-cancellation policy against them. The first level CSRs have limited power to do anything like offer discounts, upgrade service for free, etc. They can do some, but that is child's play compared to your cancellation people. What you do is if you don't work something out with the first level, tell them you want to cancel. You don't have to actually mean it, you just have to make them think you mean it. Even if there are no good alternatives ("I'll switch to satellite and DSL. I don't really need all of your bandwidth" or "My 4G hotspot works fine for me"). Sounds ridiculous, but you need to commit to the role. They will then transfer you to the cancellation people. Their job on paper is to shut off your service and close your account, but as we have seen in the news recently, their actual job is to do anything they can to prevent you doing that. If you get here, you are golden. Walk right into their trap: "Why do you want to cancel?" "I'm sorry to hear that, you must be very frustrated. What if I were to offer you x y z? Would that change your mind?" Checkmate.