Simple install the version of PS you are using on the new computer.
If that is the CC version download the Creative Cloud desktop app and log in with your Adobe ID. Once that is done all the apps you have subscribed to will be offered for install.
If it is CS6 or older just get the CD/DVD out and install it. If it is a downloaded version, you have no CD/DVD disc then download that version from the Adobe website and run the installer.
For CS6 or older you will need the license key, serial number, and if that serial number is for an Upgrade version you will need the serial number from a previous version.
Once it is installed on the new computer you can copy over your user presets and other changes you have made to PS like work spaces.