Select a ticket from your inbox and view the ticket's details on the right:

Click 'Details' to see all attributes like creation date, addressed team or agent, ticket state, etc.:

The ticket isn't locked for you to be solved. Click 'Accept' to lock it! In case another agent tries to lock this ticket at the exact same moment one of you will see an error message.

Now that a ticket is locked for you exclusively finalize the ticket and enter a short comment on your solution.:

Click 'Finalize' to close the ticket and return to the list of incoming tickets.

The ticket's owner will see the state 'closed' for this ticket in his outbox and your done comment in the tickets details. He will also see that it was you who solved the ticket.