how to expand Ubuntu partition

go to system->administration->disk utility
select the unallocated space
choose linux partition ext4
ad apply.

Yes, for expand ubuntu partition you should use Gparted Live USB (you can't operate with mounted partitions and root partition can't be unmount). Here is a guide for getting Gparted Live USB:

http://gparted.sourceforge.net/liveusb.php

There will be "Resize/Move" button. You should use it, if your ubutnu partition is neighbour to unallocated space.

P.S. Sorry for my bad english)

I tried creating a USB drive using unetbootin and got "initial menu has no labels," then "could not find kernel image: vesamenu.c32." I tried it twice (erased and reloaded) and got the same error both times. Am I missing something obvious?
GParted Live on USB site is not easy to follow (for n00bs, anyway.)

Try to use "standart" Ubuntu LiveUsb creator (in System->Administration)

I try to create Live USB using both unetbootin and standart ubuntu usb creator and i got the same error both times. I don't know what is wrong but suggest you another solution without using USB drive.

Add this to the end of /boot/grub/grub.cfg (edit it using "sudo nano /boot/grub/grub.cfg"):

menuentry "Gparted live" {
set root=(hdX,Y)
set isofile="/PATH_TO_ISO/gparted-live-0.5.2-1.iso"
loopback loop $isofile
linux (loop)/live/vmlinuz boot=live union=aufs noswap noprompt vga=788 ip=frommedia toram=filesystem.squashfs findiso=$isofile
initrd (loop)/live/initrd.img
}

where (hdX,Y) - partition, where is located iso file (X - number of hard drive, beginning with 0, X - number of partition, beginning with 1)
PATH_TO_FILE - full path to iso file

Then reboot and select last entry ("Gparted live")

I too failed, but thought it might have been the USB drive. I thought of using bootable ubuntu disk in a separate disk drive. That will have a gparted on it, and if I go through that, won't it work? Spaseba for all your effort, by the way.

Gave up on gparted boot, but DID get in with ubuntu boot and created new partition. Don't I have to move ubuntu into it, and if so, how?

If you manage to create new partition then you can delete it also.On that unallocated space expand your existing ubuntu partition.