To archive emails on Gmail, sign in to the Gmail account on your web browser. Choose the message that you want to archive. Once the mail has been selected, click the Archive icon at the top of the screen. You can also archive emails in your Gmail application. Open the Gmail app on your mobile phone. Next, select and open the message that you want to archive. At the top-right corner of the screen, tap the Archive icon. Alternatively, swipe the email left or right as per the archive settings.