The CP system has been in place for a long, long time. It is finally being threatened as an unnecessary part of the tournament system. That said, we can still milk it for all it's worth until it gets removed, if it happens.
First, you should know your character's best stages for CP options, and use them openly. Have a CP list for each character the opponent could be. Yes, for every character. It's a minimal time investment with huge pay-offs later. Write it in a notebook and memorize it. Also, have no weak stages. Just don't. Be good at all of them.
Understand that each player gets to ban a stage. This means that when you are formulating your Plan, you'll want two stages ready for a solid CP choice, as well as one ban. This is important to note because if you feel that you have some definite advantage on two stages, your opponent banning one is essentially worthless. That ban no longer has any value. You want to minimize that tool of your opponent's as much as possible, so yeah learn to CP each character to 2 stages pretty much. On the other hand, you should ban your obviously weakest stage.
Finally, understand that when you ban a stage, your opponent cannot pick it. You still can. Some TOs are shaky on this, so clear it with them in private prior to the event. If you ban a stage, your opponent will consider it banned and choose a different ban. This is brilliant because you can ban your own CP options to "protect" them later. You absolutely must win the first game to properly exploit this point. Only ever attempt this strategy after you’ve already won the first game. For example, here's your plan:
Match-up: Marth (me) vs Fox (opponent)
I, the Marth, won the first game.
Plan A:
-CP to Final Destination (first choice), and if it is banned by your opponent...
-CP to Yoshi Story (second choice)
-Ban Dreamland 64
At most events, bans are decided after game one and before game two and before any stage selection has been made. After you win your first match, you will be asked for a stage ban because loser picks stage first in slob picks. If you are unsure what the opponent will pick for his game 2 CP, then banning RC can be a good idea, or it can be a wasted ban. It is risky to decide. Instead, ban FD. While you are definitely risking losing game 2, you are also in a way securing that you will win game 3 and therefore take the set. You also get to pick your ban first because the opponent must pick a stage at that time. It then looks something like this:
Plan B:
-Ban Final Destination
-CP to Final Destination if you don't win game 2, win the set 2-1 in a secure manner.
Usually a cautious opponent will let you ban a stage first because it gives him more information when deciding what to ban for himself. In the event that your opponent decides a stage ban before you, you can stick to Plan A and take your second CP as per usual and waste that ban. Regardless of what the opponent does and at what time, it assures you to go into match 2 with the least amount of a disadvantage, and you also go into match 3 with the heaviest possible advantage. Since this is just another way to net free wins, you should abuse the ability to react here as much as possible.
Have a Plan A and a Plan B like I have above for every character. Having no "weak" stages and always having strong choices will hand you free wins repeatedly, even against players that are better than you.