In the eM Client application, go to Menu > Help > License on Windows or Help > License on macOS.

Click the ‘Activate’ button and insert your activation key (including the hyphens).

If there is no Activate button and this section already seems to include some License information it means there already is a license activated on this computer.
If it's the correct license, you don't need to do anything.

If you wish to activate a different license, simply click ‘Deactivate’ first to remove the current license. The same button will then be replaced by the ‘Activate’ option so you can proceed using the steps above.