It is possible to set up a linux system with no passwords, but it isn't completely simple or recommended (especially on systems with any internet exposure.)
First you can do away with a root password, by leaving that blank when installing. The user password is required while installing, but you can configure Linux to boot directly to the user interface by enabling automatic login, and the system will start without needing to input a password.
If you configured the system without a root password, the installer will have given sudo privileges to the user, and will promp for a password when a sudo command is input at the terminal.
With automatic login and sudo privileges for the user, you would only need to enter your password to perform administrative tasks that probably should be password protected. Otherwise you shouldn't normally need to user your password.
There are ways to even remove the requirement for a password for sudo tasks, but I've never tried and would have to google instructions how to do it. (not to mention that it's generally probably not a good idea.)