Follow the steps:
http://www.turnkeylinux.org/blog/extending-lvm
More important is the logic step:
PV[s] (Physical Volumes) -> VG[s] (Volume Groups) -> LV[s] (Logical Volumes) -> Filesystems.
There is the picture:
http://www.howtogeek.com/howto/40702/how-to-manage-and-use-lvm-logical-volume-management-in-ubuntu/
We need to first add the physical Volume, it is possible by using gparted. And then using lvm for extend the Volume Group size. Next, increase the Logical Volumes. Finally is the Filesystems by using resize2fs.
Please note the those tools (lvm, resize2fs) are located at /sbin. We need to use them by:
cd /sbin
./lvm or ./resize2fs to do this
