Start by entering the command (/register region gamename tag), as shown below. Simply fill in the appropriate details for region, gamename and tag:
You will then see the confirmation message with a summoner icon that you need to set for the account you previously specified.
Open the League of Legends client and log in if necessary. Click on the profile icon and then on your summoner icon. Scroll to the end of the list of icons and select the icon from the list that is displayed in the Zoe message.
Then close the summoner symbol selection window so that the symbol is saved.
Now click on the green Done button on Zoe's message. This should link your account.
After that, you can change your summoner profile icon back.