Here's the deal.
0.) Take / verify good backups
of important data on your system! Do not skip this step. If you're thinking of skipping this step, do not proceed.
1.) Create a new partition on /dev/sdb using fdisk(8). It's up to you whether you blow away existing partitions, and it's also up to you what size your new partition will be (perhaps 100GB for starters?). Example: # fdisk /dev/sdb
If you're not familiar with / don't want to dabble in fdisk(8), then download and burn a copy of Gparted
to create your new partition.
2.) Add the new partition to your volume group. Example: # vgextend VolGroup01 /dev/sdb2
Replace "sdb2" with the partition you just created. Don't worry about marking the new partition as a PV - vgextend(8) will take care of that for you.
3.) Extend your logical volume. Example: # lvextend -L+20G /dev/VolGroup01/LogVol00
4.) Expand your filesystem. Example: # resize2fs /dev/VolGroup01/LogVol00
Note that different OSes / versions / filesystems may use different utilities to expand the filesystem.
5.) Done. Confirm using df(1) or some such.