Here are the steps I took to upgrade to Bitcoin Core v27.0 on Ubuntu Linux

1. Login via SSH to your bitcoin core node
   ssh user@node-ip
2. Apply any operating system updates and reboot
   sudo apt-get update && sudo apt-get upgrade -y && sudo reboot
3. Log back in to your bitcoin core node via SSH
   ssh user@node-ip
4. Check your bitcoin version
   bitcoin-cli --version
5. Go to your downloads directory
   cd ~/Downloads
6. Download the release for your platform and wait for the file to finish downloading (Linux in my case)
   wget wget wget https://bitcoincore.org/bin/bitcoin-core-27.0/bitcoin-27.0-x86_64-linux-gnu.tar.gz
7. Download the list of cryptographic checksums: SHA256SUMS
   wget wget https://bitcoincore.org/bin/bitcoin-core-27.0/SHA256SUMS
8. Download the signatures attesting to validity of the checksums: SHA256SUMS.asc
   wget wget https://bitcoincore.org/bin/bitcoin-core-27.0/SHA256SUMS.asc
9. Verify that the checksum of the release file is listed in the checksums file
   sha256sum --ignore-missing --check SHA256SUMS
10. Verify that the checksums file is PGP signed by a sufficient amount of keys you trust and have imported into your keychain
    gpg --verify SHA256SUMS.asc
11. Extract the contents
    tar xvzf bitcoin-27.0-x86_64-linux-gnu.tar.gz
12. Stop bitcoind service and wait until it has completely shut down (which might take a few minutes in some cases)
    sudo systemctl stop bitcoind
13. Install the contents of the extracted bin subdirectory into the /usr/local/bin directory using the the install command
    sudo install -m 0755 -o root -g root -t /usr/local/bin bitcoin-27.0/bin/*
14. Start bitcoind service
    sudo systemctl start bitcoind
15. Check your bitcoin version
    bitcoin-cli --version