Debian USB Install
We are assuming that your USB device is indicated by /dev/sdb, and that you are interested in Debian stable (other distributions are untested, but should work).
First unmount your memory stick.
sudo umount /dev/sdb
Now download the boot.img.gz, which is necessary to make your USB device bootable:
Extract this image and write it to your USB device:
sudo zcat ~/boot.img.gz > /dev/sdb
Now mount the volume to /mnt:
sudo mount /dev/sdb /mnt
In this case a Debian Stable net-install image is used. You may also use a business card iso. Nevertheless, you should be sure to use the same version of the ISO-image as the image.tar.gz that was used before.
Download the ISO to the USB device:
Now you can unmount the volume:
cd / sudo umount /dev/sdb
You can remove the USB device, and plug it in your new system. Of course you should tell your BIOS to boot from USB.