Fedora project has created a simple script to install Fedora 7 on a USB Drive with 1GB+ capacity. To use the script you will need two things:
1. A working Fedora 7 installation. You can download the Fedora 7 DVD iso image from here. You will have to burn the image to a DVD and install Fedora 7 from it.
2. Fedora 7 Live CD. You can get the CD image for one of the two available versions here.