Commands:
vgcreate creates a new VG on block devices. If the devices were not previously initialized as PVs with pvcreate, vgcreate will initialize them, making them PVs. The pvcreate options for initializing devices are also available with vgcreate.
We create a volume group with vgcreate (Create a volume group)
# vgcreate [vg name] /dev/device /dev/device2 /dev/device3
For example
# vgcreate vg1 /dev/sdb /dev/sdc
  Volume group "vg1" successfully created
Listing the new volume group (with vgs [volume group])
# vgs vg1
  VG   #PV #LV #SN Attr   VSize   VFree
  vg1    2   0   0 wz--n-   5.99g 5.99g
Listing all volume groups (vgs)
# vgs
  VG   #PV #LV #SN Attr   VSize   VFree
  rhel   1   2   0 wz--n- <29.00g    0  
  vg1    2   0   0 wz--n-   5.99g 5.99g
Or with more details
# vgdisplay vg1
  --- Volume group ---
  VG Name               vg1
  System ID              
  Format                lvm2
  Metadata Areas        2
  Metadata Sequence No  1
  VG Access             read/write
  VG Status             resizable
  MAX LV                0
  Cur LV                0
  Open LV               0
  Max PV                0
  Cur PV                2
  Act PV                2
  VG Size               5.99 GiB
  PE Size               4.00 MiB
  Total PE              1534
  Alloc PE / Size       0 / 0    
  Free  PE / Size       1534 / 5.99 GiB
  VG UUID               uvHpRZ-BdPH-Nzxy-Lp15-VMps-fzPZ-A1bebc
Remember, you can also create a PV with vgcreate (bypassing the need to run pvcreate)
# vgcreate vg2 /dev/sdd
  Physical volume "/dev/sdd" successfully created.
  Volume group "vg2" successfully created
You can use vgextend to extend volume groups by adding physical volumes to it.
Initialize the new drive as a physical volume
# pvcreate /dev/sde
  Physical volume "/dev/sde" successfully created.
Add the new physical volume to the volume group
# vgextend vg1 /dev/sde
  Volume group "vg1" successfully extended
vgreduce removes one or more unused PVs from a VG.
Let's look at our volume group. Note it has 8.99GB of space
# vgs vg1
  VG  #PV #LV #SN Attr   VSize  VFree  
  vg1   3   0   0 wz--n- <8.99g <8.99g
Remove one of the physical volumes
# vgreduce vg1 /dev/sde
  Removed "/dev/sde" from volume group "vg1"
List the volume group again and now it has 5.99GB
# vgs vg1
  VG  #PV #LV #SN Attr   VSize VFree
  vg1   2   0   0 wz--n- 5.99g 5.99g
vgremove removes one or more VGs. If LVs exist in the VG, a prompt is used to confirm LV removal.
# vgremove vg1
  Volume group "vg1" successfully removed