In Outlook 2013 (and newer), Gmail uses the Sent folder on the server.This folder is automatically subscribed to your IMAP account; expand the [Gmail] folder to find the Sent folder.You can control what folders are visible in your IMAP clients by subscribing or unsubscribing from IMAP folders.
You need to configure the account settings online to allow IMAP (and/or POP3) at Gmail settings.
This needs configured only the first time you use Gmail. Two-way sync is enabled by default, or choose one way sync.
Beginning with Outlook 2013, you cannot choose the Sent folder; Outlook asks the IMAP server which folder it should use.
If the server supports XLIST or enhanced-list, or Outlook can match a folder on the server to it's folders by name, sent items will be stored in the Sent folder on the server, otherwise they will be in the local Sent Items folder.
If you don't use two-factor authorization on your Gmail account, you need to Allow less secure apps in Gmail settings at the end of the Gmail Security options page.