The only way to do it would be to clone your device with another. This is terribly non-trivial to the point where I'm not even sure it's still possible on modern hardware anymore.

That leaves you with the only other possibility, exploiting flaws in the crediting system.

Now, keep in mind, even if you could do either of these, it is exceedingly likely that you will get caught anyway. How? Maybe you call up your mom, maybe you visit your yahoo email account, whatever - unless you plan on leading a completely separate and error free double life, you're going to cross paths and your anonymity is gone.

I would suggest you just pay for services like everybody else rather than invest time in an activity that does come with legal ramifications should you actually 'try' anything.

If you are driven by a keen interest to understand how GSM works, then study the signaling system - both the OTA component and SS7, modulation methods, anything and everything about cellular radio. It ~will~ take you a year or more to get a good handle on the basics - and that's assuming you have several hours a day you can devote to study.