Following is step by step for installing 12.04 on a 64GB flash drive on an Intel machine. 12.10 is almost the same.
This is just like doing a normal install to internal drive except for the option of making the first partition FAT32 (or leaving it NTFS) so Windows can see it.
Turn off and unplug the computer. (See note at bottom)
Remove the side from the case.
Unplug the power cable from the hard drive.
Plug the computer back in.
Insert the flash drive.
Insert the Live CD or Live USB.
Start the computer, the CD/USB should boot.
Select language
Select install Ubuntu.
Select Download updates while installing and Select Install this third-party software.
Continue.
At "Installation type" select "Something else".
Continue
Confirm Device is correct.
Select "New Partition Table".
Click Continue on the drop down.
(Optional partition for use on Windows machine)
Click "Free space" and "Add".
Make "Size:" about 66000 MB.
Select "Primary".
Location for the new partition = "Beginning of this space".
"Use as:" = "FAT32 file system".
And Mount point = "/windows".
Select "OK"
Click "free space" and then "Add".
Select "Size:" = 4000 to 6000 megabytes, "Primary", Beginning of this space, Ext4, and Mount point = "/" then OK.
(Optional home partition)
Click "free space" and then "Add".
Select "Size ..." = 1000 to 4000 MB, "Primary", Beginning, Ext2, and Mount point = "/home" then OK.
(Optional swap space, allows hybernation)
Click "free space" and then "Add".
Select "Primary", "New partition size ..." = remaining space, (1000 to 2000 megabytes, or same size as RAM), Beginning and "Use as" = "swap area" then OK.
(Important)
Confirm "Device for boot loader installation" points to the USB drive. Default should be ok if HDD was unplugged.
Click "Install Now".
Select your location.
Continue.
Select Keyboard layout.
Continue.
Insert your name, username, password, computer name and select if you want to log in automatically or require a password.
Selecting "Encrypt my home folder" is a good option if you are worried about loosing your USB drive.
Select Continue.
Wait until install is complete.
Turn off computer and plug in the HDD.
Stick the side panel back on.
Note:
You may omit disabling the hard drive if, when partitioning you choose to install grub to the root of the usb drive you are installing Ubuntu to, (ie sdb not sdb1). Be cautious, many people have overwritten the HDD MBR.
You can update grub later, if you wish.
/
,/home
,/opt
and not/boot
. Chosesdb
as location for installing boot loader, where sdb points to your external hard disk. – Hashken Dec 10 '12 at 19:06