There are a couple of ways of doing this and it depends on how secure you need to be.
Use *67 to hide your phone number
If you are calling to bug an ex, beg for forgiveness or whatever and you just want to hear them answer the phone before hanging up, you can just use *67 as a prefix on their number. This works with most carriers in the US I believe. It just suppresses caller ID.
Use a pay phone
Then there is the call that you want to make to turn in your neighbor who is selling drugs. Just go somewhere and use a pay phone. There aren’t a lot of them, but they do exist. Don't use a credit card. Nobody is going to dig too deep into this call, but you would not be connected with it obviously. Could you be found? Absolutely.
Use a "free call" service
The Internet has also opened up another avenue. There are “free call” services which will let you dial a number for US and Canada calls from a web page without any registration. You want to do this from a public Wi-Fi location, like a Starbucks and be somewhere where you will not be overheard. Make sure the mobile device you are using has cellular data switched off to ensure it is on Wi-Fi and only Wi-Fi. If someone tracks this back to the free call service and they keep logs, they will have the IP address of the Starbucks, which is pretty much a dead end. I would make sure that I wasn’t on camera wherever I was for this.
Of course, if you are going to do things that are illegal, at some point you are likely to get caught. If you involve others in your schemes, likely they will turn on you to save themselves. Crime does pay, but eventually there is a reckoning and it can be severe.
