How to Unlock a SIM Card for Use on a Different Network?

I'm looking for guidance on how to unlock my SIM card from my current carrier to use it with a different network. What are the necessary steps, and are there any risks or issues I should watch out for? Additionally, how can I confirm that my phone is completely unlocked once I’ve finished the process?
 
I also asked this question on Facebook, and most people recommended that I contact the official SIM operator's. However, my problem still hasn't been solved. Could an expert please guide me on this?
 
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