Iniciaremos com um filesystem de nome backup e terá um disco.

1. Preparar o disco usando fdisk, abaixo o output de todo o processo:

# fdisk /dev/sdj

WARNING: DOS-compatible mode is deprecated. It's strongly recommended to
         switch off the mode (command 'c') and change display units to
         sectors (command 'u').

Command (m for help): d
Selected partition 1

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

Calling ioctl() to re-read partition table.
Syncing disks.

# fdisk /dev/sdj

WARNING: DOS-compatible mode is deprecated. It's strongly recommended to
         switch off the mode (command 'c') and change display units to
         sectors (command 'u').

Command (m for help): n
Command action
   e   extended
   p   primary partition (1-4)
p
Partition number (1-4): 1
First cylinder (1-2088, default 1):
Using default value 1
Last cylinder, +cylinders or +size{K,M,G} (1-2088, default 2088):
Using default value 2088

Command (m for help): t
Selected partition 1
Hex code (type L to list codes): 8e
Changed system type of partition 1 to 8e (Linux LVM)

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

Calling ioctl() to re-read partition table.
Syncing disks.

Para ter certeza que o processo foi feito corretamente utilize o comando:

# fdisk -l /dev/sdj

Disk /dev/sdj: 17.2 GB, 17179869184 bytes
255 heads, 63 sectors/track, 2088 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0x1b58e145

   Device Boot      Start         End      Blocks   Id  System
/dev/sdj1               1        2088    16771828+  8e  Linux LVM

2. Criando o PV:

# pvcreate /dev/sdj1

  Physical volume "/dev/sdj1" successfully created

3. Criando o VG:

# vgcreate backup_VG /dev/sdj1

  Volume group "backup_VG" successfully created

4. Criando o LVOL:

# lvcreate -L 15.5G -n backup_LV backup_VG

  Logical volume "backup_LV" created

As opções -L se refere ao tamanho e a opção -n ao nome do VG

5. Formatando o volume recém criado:

# mkfs.ext4 /dev/backup_VG/backup_LV /backup/

mke2fs 1.41.12 (17-May-2010)
mkfs.ext4: invalid blocks count - /backup/

# mkfs.ext4 /dev/backup_VG/backup_LV

mke2fs 1.41.12 (17-May-2010)
Filesystem label=
OS type: Linux
Block size=4096 (log=2)
Fragment size=4096 (log=2)
Stride=0 blocks, Stripe width=0 blocks
1015808 inodes, 4063232 blocks
203161 blocks (5.00%) reserved for the super user
First data block=0
Maximum filesystem blocks=4160749568
124 block groups
32768 blocks per group, 32768 fragments per group
8192 inodes per group
Superblock backups stored on blocks:
        32768, 98304, 163840, 229376, 294912, 819200, 884736, 1605632, 2654208

Writing inode tables: done
Creating journal (32768 blocks): done
Writing superblocks and filesystem accounting information: done

This filesystem will be automatically checked every 37 mounts or
180 days, whichever comes first.  Use tune2fs -c or -i to override.

6. Montado o filesystem:

# mkdir /backup
# mount /dev/backup_VG/backup_LV /backup
# df /backup

Filesystem                      1K-blocks   Used Available Use% Mounted on
/dev/mapper/backup_VG-backup_LV  15997904 170736  15014524   2% /backup

Agora basta incluir na fstab para quando o servidor sofrer reboot, o filesystem montar.