The service is still in beta has been rolled out to limited users on Wednesday. Users who emailed firstname.lastname@example.org could request an invitation, but earlier only Google employees had the ability to invite others. But now it has been changed.
If you have Inbox, just hover over the "+" icon (or tap it on iOS or Android), and look for the golden-ticket icon above the "Compose" icon. It says "Invite to Inbox." Select it and enter the email address of the person you want to invite.
All Inbox users now have three invites they can share. To give away yours simply start a new email from within the Inbox app and tap the 'Invite to Inbox' option that’s depicted by a golden ticket. You can then select the email address you’d like to send the invite to and then tap the 'Invite' button.
If you haven’t yet received an Inbox invitation, you can request yours by emailing email@example.com. It’s still unclear when Google intends to make the service widely available to all.