Inbox is invite-only at the moment, but you can request one from firstname.lastname@example.org or get one from a friend who has invites to spare. The service will be available on the Web (Chrome only), iOS 7+ and Android 4.1+. Versions for tablets and other modern browsers are also in the works.
Google doesn’t intend for Inbox to replace Gmail. Actions you take in either product will show up in the other. Inbox uses your existing Gmail and Google usernames.