Updating the firmware is quite easy, you basically copy the new image on the router, install it into the flash and reboot the router.
Copying the firmware on the router is the main challenge. We have described a few ways below.
We assume that you have a working Ethernet connection to the router, running a Linux host PC. It may also work in Windows/Mac if you have the nc (netcat) tool avaliable.
On your host, start a netcat server on some port and pipe the .bin firmware file into it:
$ nc -l -p 5555 < /path/to/openwrt-...-sysupgrade.bin
Now open a ssh/telnet/serial connection to the router and download the image file:
# cd /tmp nc <ip> 5555 > image.bin
Where <ip> is the IP address of the host PC.