Messages sent through the Gmail account will sync down to Outlook on the next sync, or when you open the Sent folder.
If you use Gmail's SMTP server, Gmail will put a sent copy in the [Gmail]/Sent Mail folder automatically.
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.
The recommended method of using Gmail accounts in Outlook is to use IMAP.
However, this only syncs email, not your Gmail calendar and contacts.