You'll need a bootable USB drive (they almost all are and the easiest way to find out if yours will work is just to try it) and a computer that can boot from USB (any computer build in the last five years should be able to).
1. Go to http://software.opensuse.org/ and get a copy of the installer. Make sure you choose the correct type of computer. On AMD/Intel chips, 32-bit will always work and 64-bit will work on most newer computers.
You can choose to use either the DVD or the network install. If you choose the DVD option, you'll need a USB drive with a capacity of at least 4.2GB. Practically, 8GB is the smallest USB drive you'll find with enough space. If you choose the network install, you'll need a network connection during the installation. In my experience, an ethernet connection always works and a wireless connection is somewhat iffy (although the Eee PC wireless card works perfectly).
2. Install the required packages. As root (the rest of the steps require you to be root as well):
yast -i syslinux lilo
3. Mount the installation image:
mount openSUSE-11.1-NET-i586.iso MOUNT_POINT -o loop
where MOUNT_POINT is any directory and openSUSE-11.1-NET-i586.iso is the name of the file that you downloaded.
4. The mkbootdisk program copies the files to the USB drive and makes the drive bootable.
mkbootdisk --32 --partition /dev/USB_DRIVE MOUNT_POINT
where USB_DRIVE is the partition you want to copy the files to. On my system, this was /dev/sdc1. If you're installing a 64-bit system, then replace "--32" with "--64".
5. Do a little bit of cleanup:
umount MOUNT_POINT && rmdir MOUNT_POINT
You now have a bootable USB drive with a copy of the openSUSE installation media.