it is possible to make a full disk image with running ubuntu with following command:
dd if=/dev/sda of=/image_name
After i make it, how can i restore that image on a crushed system?
Boot from the live cd. Mount your destination media to (say) /mnt.
dd if=/dev/sd whatever of=/mnt/mybackup.ddimg
dd if=/mnt/mybackup.ddimg of=/dev/sd wharever
The destination drive should be the same size or bigger than the original.
A better way is using tar.
Mount the source to /mnt, mount the destination to /home (say)
tar cvfpz /home/mybackup.tar.gz /mnt
This can then be restored to any size drive:
tar xvfpz /home/mybackup.tar.gz
(After mounting source to /home and destination to /mnt.)
Then just install grub.
In addition to hatterman's great answer you can compress the image as it's taken using
gzip like this:
dd if=/dev/sdx | gzip > /mnt/mybackup.ddimg.gz