How to Extend Volume Group / Adding physical volumes to a volume group

For increasing the volume group size create another partation in the same disk or in a separate disk,

# vgdisplay
  --- Volume group ---
  VG Name               vg-ctechz
  System ID
  Format                lvm2
  Metadata Areas        2
  Metadata Sequence No  16
  VG Access             read/write
  VG Status             resizable
  MAX LV                0
  Cur LV                1
  Open LV               1
  Max PV                0
  Cur PV                2
  Act PV                2
  VG Size               1.04 GB
  PE Size               4.00 MB
  Total PE              266
  Alloc PE / Size       188 / 752.00 MB
  Free  PE / Size       78 / 312.00 MB
  VG UUID       ui4JTr-JOwC-VCvG-5Evc-poOD-3Klr-hM3feq

[root@localhost ~]# vgs
  VG        #PV #LV #SN Attr  VSize VFree
  vg-ctechz  2   1   0 wz--n- 1.04G 312.00M

# fdisk -l

Disk /dev/sda: 31.8 GB, 31890341888 bytes
255 heads, 63 sectors/track, 3877 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes

   Device Boot  Start End  Blocks   Id  System
/dev/sda1   *    1    3315 26627706 83  Linux
/dev/sda2       3316  3446 1052257+ 82  Linux swap/Solaris
/dev/sda3       3447  3520 594405   8e  Linux LVM
/dev/sda4       3521  3582 498015   8e  Linux LVM

# fdisk /dev/sda

The number of cylinders for this disk is set to 3877.
There is nothing wrong with that, but this is larger than 1024,
and could in certain setups cause problems with:
1) software that runs at boot time (e.g., old versions of LILO)
2) booting and partitioning software from other OSs
   (e.g., DOS FDISK, OS/2 FDISK)

Command (m for help): n
Command action
   e   extended
   p   primary partition (1-4)
e
Selected partition 2
First cylinder (3316-3877, default 3316):
Using default value 3316
Last cylinder or +size or +sizeM or +sizeK (3316-3446, default 3446): +600M

Command (m for help): p

Disk /dev/sda: 31.8 GB, 31890341888 bytes
255 heads, 63 sectors/track, 3877 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes

    Device Boot  Start  End Blocks   Id  System
/dev/sda1   *    1     3315 26627706 83  Linux
/dev/sda2       3316   3389 594405   5   Extended
/dev/sda3       3447   3520 594405   8e  Linux LVM
/dev/sda4       3521   3582 498015   8e  Linux LVM

Command (m for help):
Command (m for help): w
The partition table has been altered!

Calling ioctl() to re-read partition table.

WARNING: Re-reading the partition table failed with error 16: Device or resource busy.
The kernel still uses the old table.
The new table will be used at the next reboot.
Syncing disks.

# partprobe

then create the new partition inside the extended partition,

# fdisk /dev/sda2

# fdisk -l

Disk /dev/sda: 31.8 GB, 31890341888 bytes
255 heads, 63 sectors/track, 3877 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes

   Device Boot Start  End   Blocks   Id  System
/dev/sda1   *  1      3315  26627706 83  Linux
/dev/sda2      3316   3389  594405   5  Extended
/dev/sda3      3447   3520  594405   8e  Linux LVM
/dev/sda4      3521   3582  498015   8e  Linux LVM
/dev/sda5      3316   3352  297171   83  Linux

sda5 is the new partation,

# pvcreate /dev/sda5
  Writing physical volume data to disk "/dev/sda5"
  Physical volume "/dev/sda5" successfully created

# vgs
  VG        #PV #LV #SN Attr   VSize VFree
  vg-ctechz   2   1   0 wz--n- 1.04G 312.00M

to extend vg # vgextend oldvgname /dev/newvgname

# vgextend vg-ctechz /dev/sda5
  Volume group "vg-ctechz" successfully extended

# vgs
  VG        #PV #LV #SN Attr   VSize VFree
  vg-ctechz   3   1   0 wz--n- 1.32G 600.00M

Check the old vgsize and new vgsize here its extended 
from 1.04G to 1.32G