An LVM volume group is an abstraction of a hard drive, or multiple hard drives, or multiple RAIDs, or... It's really a separate question, so I don't think it's pertinent to get more detailed than that here.
The point is, both LVM groups and hard drives can contain partitions. Which way you go is a matter orthogonal to your main question.
The easiest way to make
/home a separate partition is to do it during OS installation, with a complete hard drive repartition and format pass. You can change your mind and make
/home separate later, but it's more work.
The way you create a separate
/home partition differs depending on the particular OS installer, but these days, you typically have to tell it you want to do an "advanced" hard drive setup, overriding its simple defaults. You can then choose to reserve some amount of hard drive space for
/home and leave the rest of the disk (or LVM group, or RAID, or...) to the rest of the system.
/home a separate partition after you've installed the OS, you either have to repartition or add another volume. Just as a simple example, you could insert a USB stick and put
/home on it like this:
(assume the USB stick is /dev/sdc, mounted on /media/usb)
# umount /media/usb
# mke2fs -j -L /home /dev/sdc1
# mount /dev/sdc1 /media/usb
# cd /home
# find . -print | cpio -mpud /media/usb
# umount /media/usb
# mount /dev/sdc1 /home
What we've done so far is reformat the USB stick with a fresh ext3 filesystem, then copied the entire contents of
/home over to it while preserving all permissions, timestamps, etc. Then we've laid the new
/home copy over the top of the old for testing. Once you're satisfied that it works, you could unmount
/dev/sdc1, nuke the old
/home and remount the new one.
Beware, this is dangerous. I am presenting it as an example, not a recommendation.
Also dangerous is repartitioning the drive after it's already been formatted. You'd have to do that if you wanted to move
/home to a new partition without adding another volume to the machine. The
gparted tool can do this, but it's not without risks. Having opened up space for a new partition and created it with
gparted, you could do something much like I show above to move the contents of the old
/home directory to the new partition.
You should also beware that making
/home separate has its own problems. One is, it forces you to set aside a slice of your disk for
/home and then live with it. It's easy to get too clever with partitioning; you could end up with like 10 partitions, 8 of which are full and 2 which have less than 10% usage, and no easy way of reassigning space from the empty ones to the full ones. LVM and
gparted each provide some solutions to this, but the important point to keep in mind is, be very sure you need the extra partitions. The more moving parts, the more things there are to break.