You can set on the
Configuration -> General Settings page how tickets are assigned (under Auto assign). You can choose to disable this, assign manually, assign to the creator or editor, the default agent (which can be set for ticket types on the
Configuration -> Ticket Content page), or use a more advanced routing algorithm. Note that round robin and load balancing currently only work for emailed tickets.
The reason you're seeing 'My ticket' probably means you're currently not an (or an inactive) agent, and thus can only see tickets created by (or for) yourself. For more advanced permissions for tickets you'll have to check the
Configuration -> User Access & Roles page.
Indeed as greenangel says, this page may help:
http://www.lansweeper.com/kb/175/introduction-to-the-help-desk.html.