Google Inbox launched a while back, providing a new feel for Gmail accounts, but so far it's been limited to invitations - which you can obtain by emailing Google, or by asking a friend with Inbox for one of their invites.
Haven't been able to get access to Inbox yet? Fear not, Google's giving away invites to Inbox for the next few hours.
reddit AMA starting now. Also, anyone that sends an email to firstname.lastname@example.org from a @gmail address 10 to noon pst gets an invite today— Inbox by Gmail (@inboxbygmail) December 3, 2014
To get Inbox, do the following BEFORE 3PM EST today:
1) Login to your Gmail account
2) Email email@example.com asking for an invite.
3) And you're done! An invite should be given to you today. Emphasis on the "should".