If your email address isn't verified, you'll see a pop-up when you log into the client. Make sure the email at the top is yours:
If the email is yours:
1. Click the "Send Email" button at the bottom of the pop-up
2. Check your email for a message from Leagueoflegends@email.accounts.riotgames.com
3. Click the "Verify email" button in the center of the message
4. After a few seconds, the in-client pop-up should display a green checkmark
5. Click "Finish" at the bottom and you're good to go!
If the email at the top is not yours:
1. Click the "Change your email" hyperlink near Braum's hand
2. In the top two boxes, enter your new email. In the bottom, enter the account's password (what you log in with)
3. Click "Submit" at the bottom
4. The next page is a confirmation. If you don't get an email, you can click "Resend" at the bottom of the pop-up
5. Check your email for a message from Leagueoflegends@email.accounts.riotgames.com
6. Click the "Verify email button in the center of the message
7. After a few seconds, the pop-up should display a green checkmark.
8. Click "Finish" at the bottom and you'll be good to go!