When installing to an external drive you must be careful where you install grub! By default it will be installed to the internal drive and you don't want that.
You must first see what designation Ubuntu gives to the external. You should be able to do that by running:
sudo fdisk -l
With the external plugged in. Since it lists the size of the drives it should be easy to identify the external.
This would also be an excellent time to describe drive and partition designations in Ubuntu:
Drives are designated as /dev/sda, /dev/sdb, /dev/sdc, etc. the last letter indicates the drive number, eg: /dev/sda = drive #1 /dev/sdb = drive #2 /dev/sdc = drive #3
Partititions are designated with a number following the drive designations, eg: /dev/sda1 = drive #1/partition #1 /dev/sda2 = drive #1/partition #2 /dev/sdb1 = drive #2/partition #1
It is almost never a good idea to install grub to a partition!
Once you know the proper designation you can go ahead with the install, but when you get to the last screen you'll see an Advanced button in the lower right hand corner:
http://members.iinet.net.au/%7Eherman546/p22/035.png
Click on it and you'll see that you can "toggle" through a list of devices:
http://members.iinet.net.au/%7Eherman546/p22/036.png
Be sure to select the proper device!
Credit here for the screenshots:
http://members.iinet.net/~herman546/index.html