The above answer is probably the simplest but if you want more than 4GB persistence:

Boot Live CD or Live USB.

Plug in flash drive.

Start gparted.

Create 2 GB FAT32 partition, (on the left side of the bar). (size is optional, extra space can be used for file storage and transfer to Windows machines).

Create a 4 GB ext2 partition to the right of this, labeled it "casper-rw". (ext3 and ext4 also work).

Create a partition in the remaining space and label it "home-rw". (optional, creates a separate home partition)

Close gparted.

Un-mount and re-mount flash drive.

Start "Create a live usb startup disk", (usb-creator).

Select "Discard on shutdown".

Press "Make Startup Disk.

When usb-creator finishes replace the contents of the file syslinux.cfg with:

default persistent
label persistent
  say Booting a persistent Ubuntu session...
  kernel /casper/vmlinuz
  append  file=/cdrom/preseed/ubuntu.seed boot=casper persistent initrd=/casper/initrd.lz quiet splash noprompt --

Shutdown, remove CD, reboot.

First time booting you can go to users and groups and create an account with yourself as an Administrator, with password if desired.

Note: The above code will bypass the Try/Install and Language screens.