You can do a Persistent install using Startup disk creator however a Full install has several advantages, it can be upgraded/updated, is more secure, and boots much faster than a Persistent install, also a Persistent install is initially limited to a 4GB persistence) file as it is FAT32. Persistence can be increased by using an ext2 partition named casper-rw to replace the casper-rw file.
Following is step by step for installing 13.04 on a 8GB flash drive on an Intel machine.
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 "+".
Make "Size:" about 1000 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 "+".
Select "Size:" = 5000 to 7000 megabytes, "Primary", "Beginning of this space", Ext4, and Mount point = "/" then OK.
(Optional home partition)
Click "free space" and then "+".
Select "Size:" = 1000 to 4000 MB, "Primary", Beginning, Ext2, and Mount point = "/home" then OK.
(Optional swap space, allows hibernation)
Click "free space" and then "+".
Select "Size:" = remaining space, (1000 to 2000 megabytes, or same size as RAM), "Primary", "Beginning of this space" 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, computer name, username, password and select if you want to log in automatically or require a password.
Requiring a password to log in and selecting "Encrypt my home folder" are good options 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 revise grub later, if you wish.