Add disk/LUN to server. Have a look at Rescan SCSI bus for scanning the SCSI bus online. Alternative reboot the server.

Prepare PV's with

pvcreate /dev/<device>

For FC LUN's use /dev/mapper/mpath<x> according to Red Hat DM Multipath Configuration & Administration

Create VG

vgcreate <vgname> -s <Physical Extent size> <path to PV>

Create LV

lvcreate --name <lvname> --size <xx>G <vgname>

Create filesytem

EXT FS:

 mkfs.ext4 -F -b 4096 /dev/<vgname>/<lvname>

Depending on distribution use relevant ext2/ext3/ext4 file system type.

XFS FS:

 mkfs.xfs /dev/<vgname>/<lvname>

Extend the disk on the underlying infrastructure (SAN LUN / Virtulization platform)

Make OS detect the changed disk size

echo 1 > /sys/block/<device>/device/rescan

Where the <device> paramter is the physical disk eg. sdb

Resize Physical Volume

 pvresize /dev/<device>
 

If LUN is under multipath:

 multipathd resize map <multipath_device>
 

Where <multipath_device> is mpath<x> or wwid depending on multipath configuration.

Extend Logical Volume

  lvextend -l 100%VG <lvname>

check man lvextend for further options

Extend filesytem which resides on Logical Volume

EXT FS:

 resize2fs /dev/<vgname>/<lvname>

XFS FS:

  xfs_growfs /dev/<vgname>/<lvname>

https://access.redhat.com/kb/docs/DOC-9855

Determine which LV is in use by swap space

grep swap /etc/fstab
Example of output:
/dev/mapper/VolGroup00-LogVol01 swap                    swap    defaults        0 0

Disable swap:

swapoff /dev/mapper/VolGroup00-LogVol01

Resize swap space.

In this example swap spaze is adjusted to 4GB.

lvresize -L 4G /dev/mapper/VolGroup00-LogVol01

Setup swap area on LV

mkswap /dev/mapper/VolGroup00-LogVol01

Enable swap space again

swapon /dev/mapper/VolGroup00-LogVol01

Verify with top or /proc/swaps:

top

output:
top - 13:32:16 up 14 min, 2 users, load average: 0.22, 0.08, 0.02
Tasks: 138 total, 2 running, 136 sleeping, 0 stopped, 0 zombie
Cpu(s): 4.2%us, 1.5%sy, 0.0%ni, 93.0%id, 1.1%wa, 0.0%hi, 0.1%si, 0.0%st
Mem: 3925256k total, 486996k used, 3438260k free, 102092k buffers
Swap: 4194296k total, 0k used, 4194296k free, 118264k cached

cat /proc/swaps
Filename                                Type            Size    Used    Priority
/dev/dm-1                               partition       4194296 0       -1