Make partitions in fdisk 

Create the physical volume
# pvcreate /dev/sda6

Figure out your current volume group
# vgscan

See what physical volumes there are (the one you created before with pvcreate should show up)
# pvscan

Set all volume groups to be active
# vgchange -a y

Create a volume group
# vgcreate vg_home /dev/sda6

Re-do pvscan/vgscan to see that vg_home exists and /dev/sda6 is in use by it
# pvscan
# vgscan

See what logical volumes there are
# lvscan

Create a logical volume inside of the volume group made earlier using 100% of free space in that group
# lvcreate -l 100%FREE vg_home

Check lvscan again to make sure the new one shows up properly
# lvscan

Since I forgot to name the logical volume, remove it and create a new one with the right name
# lvremove /dev/vg_home/lvol0

# lvcreate -l 100%FREE -n lv_home vg_home

Create a filesystem on this logical volume
# mkfs.ext4 /dev/mapper/vg_home-lv_home

Now, test mount that - congrats you can leave this as is and use it as your new /home or whatever if you'd like.
# mount /dev/mapper/vg_home-lv_home /mnt

But I want to merge this new space into my existing volume group vg_maleah
# umount /mnt

Mark lv_home as inactive...
# lvchange -a n /dev/vg_home/lv_home

Now lvscan to see that it is inactive
# lvscan

Now try to merge vg_home into vg_maleah
# vgmerge vg_maleah vg_home

Oops, can't do that because my extent sizes differ... so let's detroy that and create it better:
# lvremove /dev/vg_home/lv_home
# vgremove /dev/vg_home

Second time creating this... should go quicker - just make sure extent size matches the other
# vgdisplay vg_maleah | grep "PE Size"
# vgcreate -s 32 vg_home /dev/sda6
# vgmerge vg_maleah vg_home

Make sure the new physical volume is appearing in the proper volume group now.
# pvscan

Since it does, let's extend the logical volume that is on that volume group.
# lvdisplay

lvdisplay shows that I have two logical volumes: lv_root and lv_swap.
Since I am happy with the size of my lv_swap, I'm going to add all the space from the new
physical volume that I just added to my vg_maleah volume group to the logical volume
lv_root.

I want to use 100% of the available space.
*May or may not need to specify /dev/sda6 @ the end of this... I didn't seem to need to, since
it just used 100% of the remaining free space in vg_maleah
# lvextend -l +100%FREE /dev/vg_maleah/lv_root

Now I need to make sure and extend the filesystem that is there
Mount the filesystem read-only so we can fsck it
# mount -f -o remount,ro /dev/vg_maleah/lv_root
# e2fsck -f /dev/vg_maleah/lv_root

Verify what the minimum size for it could be...
# resize2fs -P /dev/vg_maleah/lv_root 

Resize it
# resize2fs -p /dev/vg_maleah/lv_root

Remount it
# mount -o remount,rw /dev/vg_maleah/lv_root

Done!



Other things:
Renaming a vg or lv:
# vgrename vg_currentname vg_newname
replace vgrename with lvrename...