First, create your partition as you normally would. No need to set up a FileSystem on it.
In my case I’ll try to extend my vg01-var.
vgextend vg01 /dev/sdb1
lvextend /dev/vg01/var /dev/sdb1
My sdb1 was already lvmed into something by someone, so I had to umount and to stuff:
vgchange -a n vg02