How to get a bitcoin address from a private key?

Could you please elaborate on the process of obtaining a Bitcoin address from a private key? I understand that a private key serves as the fundamental identifier for a user's Bitcoin wallet, but how does one actually derive the corresponding Bitcoin address from this key? Is there a specific algorithm or software tool that's typically used for this purpose? Additionally, is it safe to do so, and what measures should be taken to ensure the security of the process? Your insight into this matter would be greatly appreciated.