If you've already installed linux onto /dev/sda1, you can't put LVM on top of it.
LVM is created first.
The following example creates an LVM layout, which should be created from a livecd, or rescuecd
pvcreate /dev/sda1 # initializes /dev/sda1 for LVM
vgcreate vgname /dev/sda1 # creates Volume Group with one device
lvcreate --name boot --size 1G vgname # create logical volume to boot from
lvcreate --name root --size 6G vgname # create logical volume for / fs
lvcreate --name swap --size 1G vgname # create logical volume for swap
lvcreate --name home --size 2G vgname # create logical volume for /home fs
Adjust sizes to suit
Then run the Debian installer, selecting advanced partitioning and select each logical volume, set the filesystem type, indicate that formatting is needed, and install.
If you already have a substantially configured system, you could make a backup of your file systems, follow the above to create the VG,LVs, and then restore the data (both using livecd or rescuecd). After which you'll need to mount the root LV and update the fstab with new UUIDS, follow the chroot procedure to change to new LV layout and update-grub
I think squeeze can boot from a LV, but check the Debian website first, or else you'll need a separate partition for /boot that's not part of the LV.
This would be a good time to switch to GPT disk labeling for finer granularity