This is something that is really usual situation when you don’t have enough space on your guest machine and there is no anything you can delete. First thing you have to do is to add new disk using VMware's management tools. Now you have two options
1. Reboot system to newly added disk can be seen in configuration
2. Rescan scsi bus for new changes
Of course that you will use second method. Reboot is almost never possible when you are in production environment. To rescan scsi bus you have to determine how many hostX you have

[root@setenforce ~]# ls /sys/class/scsi_host/
host0 host1 host2

In my case I have 3 hosts, so I need to rescan all of them:

[root@setenforce ~]# echo "- - -" > /sys/class/scsi_host/host0/scan
[root@setenforce ~]# echo "- - -" > /sys/class/scsi_host/host1/scan
[root@setenforce ~]# echo "- - -" > /sys/class/scsi_host/host2/scan

After rescan you can see newly added disk.

[root@setenforce ~]# fdisk
Disk /dev/sdc: 5368 MB, 5368709120 bytes
255 heads, 63 sectors/track, 652 cylinders
Units = cylinders of 16065 * 512 = 8225280 bytes

Disk /dev/sdc doesn't contain a valid partition table

Next step is to create LVM partition on this disk. Here we go!

[root@setenforce ~]# fdisk /dev/sdc
Command (m for help): n I want to add new partition so I coose n
Command action
    e extended
    p primary partition (1-4)
p I want to create new primary partition so I coose p
Partition number (1-4): 1 This is first partition on this disk so I define it as 1
First cylinder (1-652, default 1): Default value so just press Enter
Using default value 1
Last cylinder or +size or +sizeM or +sizeK (1-652, default 652): Default value so just press Enter
Using default value 652

Command (m for help): t Define type of disk
Selected partition 1
Hex code (type L to list codes): 8e This will be part of LVM so code is 8e
Changed system type of partition 1 to 8e (Linux LVM)

Command (m for help): w Write changes to disk
The partition table has been altered!

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

If you run fdisk now you will see that disk /dev/sdc1 is not available to system jet, you have to run partprobe to re-read partition

[root@setenforce ~]# partprobe

On this system i have just one volume group - VolGroup00. I hae to extend this group with my /dev/sdc1.

[root@setenforce ~]# vgextend VolGroup00 /dev/sdc1
   No physical volume label read from /dev/sdc1
   Physical volume "/dev/sdc1" successfully created
   Volume group "VolGroup00" successfully extended

Running lvscan will show you currently active logical volumes on your system

[root@setenforce ~]# lvscan
   ACTIVE '/dev/VolGroup00/LogVolRoot' [39.84 GB] inherit
   ACTIVE '/dev/VolGroup00/LogVolVar' [10.00 GB] inherit
   ACTIVE '/dev/VolGroup00/LogVolSwap' [10.00 GB] inherit

I will increase LogVolRoot with 100% free extents in volume group

[root@setenforce ~]# lvextend -l +100%FREE /dev/VolGroup00/LogVolRoot

The last thing you have to do is to resize FS (ext3) on /dev/VolGroup00/LogVolRoot

[root@setenforce ~]# resize2fs /dev/VolGroup00/LogVolRoot