Lots of caveats here. While Ubuntu's upgrade process has gotten much better, there are still annoyances. Now based on experience with multiple upgrades, including most recently from Ubuntu 20.04 LTS to 22.04 (the most current LTS as of this update).
Do your homework. There's nothing more discouraging long into an upgrade but to learn that some favorite app or service is no longer supported. Have a list like "Useful Software" with the names and web site urls of everything you may need to restore afterwards (here is mine).
First, update your system to the latest packages for its current version:
$ sudo apt update
$ sudo apt upgrade
$ sudo apt dist-upgrade
$ sudo apt autoremove
Make sure update-manager-core is installed (core does not require the gui desktop):
$ sudo apt-get install update-manager-core
Finally, kick off the upgrade:
$ sudo do-release-upgrade -d
Follow the promps (in most cases accept the default, but read carefully).
At the end you'll be promted to reboot. Do that and then check lsb_release -a to verify you're at the latest LTS release.
References:
Alex Garnett. "How to Upgrade to Ubuntu 22.04 Jammy Jellyfish". Digital Ocean Community, 25 April 2022, https://www.digitalocean.com/community/tutorials/how-to-upgrade-to-ubuntu-22-04-jammy-jellyfish (this is the guide I followed at the CLI for both Server and Desktop).
Awais Khan. "How to Upgrade Ubuntu 20.04 LTS to Ubuntu 22.04 LTS". Linuxhint, https://linuxhint.com/upgrade-ubuntu-22-04/ (another great write-up using the CLI).
"Upgrade Ubuntu Desktop". Ubuntu Tutorials, https://ubuntu.com/tutorials/upgrading-ubuntu-desktop#1-before-you-start (for Ubuntu Desktop only, exclusively uses the GUI).