At the very top of the Odoo application, just under the address bar in the browser, you will see a message that informs you of how much longer your trial version of Odoo will run before you need to register. Also, remember that it is possible to lose this instance of Odoo before the time runs out, as seen here:
Clicking on the Activate by email link will send a message to the email address that you provided, containing a link to activate your Odoo database. Currently, you may use Odoo for free as long as you only install one application.
Odoo SA has experimented quite a bit with different trial terms, so do not be surprised if the trial options are slightly different by the time you are reading this.