Making a bootable USB of Ubuntu

Introduction
If your computer can boot from USB, then you can save yourself a CD by using UNetbootin to "burn" the disk image (the Ubuntu .iso file) to USB. This method has the advantage of not wasting a blank CD and of getting a snappier performance during the live session, since USB can usually be read faster than optical drives.
Things to know first

• Your USB drive should be formatted as FAT32 or FAT16. It cannot be formatted as NTFS, HFS+, or Ext4. Most USB drives come formatted as FAT32 or FAT16 already, so this shouldn't be a big worry.
• Some USB sticks come with firmware that will prevent USB booting of Ubuntu from working. It's called U3. You can read more about it (including how to remove it) on Wikipedia.
• I've used this for USB sticks, a Sansa Clip MP3 player, and an SD card. It's a pretty versatile boot method. Just make sure you have at least 800 MB of free space on the drive.
• Most recently made computers can boot from USB. If you have to burn a CD, go to the CD burning page. (As far as I know, Macs will not boot non–OS X hard drives from USB, so you will have to burn a CD.)
• If your computer's BIOS does not support booting CDs or USB, you may have to employ a workaround called PLoP. I've never used this before, and it looks complicated to me, so your mileage may vary. 

Using UNetbootin

The unetbootin-windows-###.exe file you download isn't an installer file. It's the actual program. So go ahead and double-click it to start UNetbootin.
You'll then be presented with two options. You can either select Ubuntu from the distribution list and leave it up to UNetbootin to download the Ubuntu .iso for you or, if you already have the .iso downloaded, select the .iso yourself.

Once you've done that, select the USB drive you want to "burn" the .iso to, and then click OK.

Most of the files will copy quickly to your USB drive. If you notice it stays a bit long on a file called filesystem.squashfs, don't worry. That is a normal (it's a huge file).

You can, of course, reboot immediately once it's done.

If you choose to wait on the reboot, you can take a look at the contents of your USB drive, and you should see a bunch of lowercase filenames like these.
Now your USB drive is ready to boot Ubuntu up!
To get your BIOS to boot from USB, you may have to press a special key right when you bootup (it could be F9, Escape, Delete, or F12, depending on what you have).