I have a Eee PC 1005PX.

I want to install Debian.

From another computer, I downloaded the ISO, then used:

dd if=debian-6.0.2.1-i386-netinst.iso of=/dev/sdb1

I've set the BIOS to boot from the USB device, but I just get this message:

"Reboot and Select proper Boot device or Insert Boot Media in selected Boot device and press a key"

I've also tried using this:

cat debian.iso > /dev/sdb1

After creating the USB from the ISO, the USB seems fine, has files inside it just like a normal CD made from an ISO.

How can I get this working?

You've copied to /dev/sdb1. That means you did not touch the MBR that should say partition 1 is bootable (or something like that.

try with /dev/sdb instead (but unmount /dev/sdb1 first).

I don't use your distro, but fedora instead, and in my distro there is a tool for making bootable usb drives from isos.
I think recent isos can be copied with dd to create a bootable usb drive, so just use /dev/sdb and you should be fine

Works. Thank you.