Always make sure that your eeePC has a full battery and is connected to the power before doing an upgrade!
You use this tutorial completely at your own risk!
The bios that comes with the eee pcs is updated from time to time by asus, so it can be beneficial to install the newest version. You can get the newest version of the BIOS for EeePC 904HD from the asus support site. Click the plus sign left of BIOS, and it will show all the versions from newest to oldest. Note that I'm talking about EeePC 904HD (that's what I own), if you have 901 or some other model and update it with 904HD BIOS, there's a good chance you'll make your laptop unusable. Make sure you find the page for your own model in asus's site.
Now the next step is more difficult. You have to format a USB stick to FAT16 and make sure that the new FAT16 partition is less than 32 MB (make it 16 MB to be safe, the ROM file is only 512K anyway) . Then copy the ROM file and rename it to "904HD.ROM".
Finally, leave the USB stick attached to the laptop and reboot. As soon as you see the BIOS splash screen press Alt+F2. The BIOS will read the file and reflash. You should see this message
EZ-Flash starting BIOS update
Checking for USB device
USB Device found
Reading file "701.ROM". Completed
It will take some time, during which just don't touch your laptop. After the update has finished the laptop
will turn off.
