How to enroll to the course without asking for that course' teacher?

To join the course go to the course list first. Then click to the drop list on the course name and choose "send request".
You will be transfered to the group menu. Click on the "members" group.

After you choose Actions->Join the Group you will be able to access  all course content. Note it will be possible to do only if members group is configured for that purposes by the course teacher (see How to make course available for any LMS user to subscribe? question)