You are dealing with "partitions" and "logical volumes" here. Before recommending anything I want to make sure you know the difference. I can't tell for sure if you know this by your questions. No offense intended ... I just don't want to send you down the wrong path by making an assumption.
Your disk has two partitions, one that's 100Mb and one that's 16Gb. The larger one is an LVM physical volume, type 8e. The smaller one is Linux native (ext2, ext3, reiser, etc.), type 83.
That 16Gb partition is divided up into two logical volumes, one that's 512Mb and on that's 15.34Gb.
Just judging by sizes, my guess is that hda1 is mounted as /boot, LogVol01 is mounted as /swap, and LogVol00 is mounted as /
If all the above is not 100% understandable, it would be best to tell us exactly what you plan to use that 1Gb new space for, and also provide the output from the following commands:
# fdisk -l
If the above is all obvious to you and you already understand LVM, then the answer to your original question on how to make a new 1Gb partition
would be: (1) reduce the filesystem on the larger LV, then (2) reduce your larger LV, then (3) reduce your VG, then (4) reduce the partition containing the VG, then (5) create your new partition.
It's considerably simpler if you only want a new 1Gb logical volume. Steps (1) and (2) as above, then (3) create a new LV.