Once the latest firmware is up on your boot server, all you need to do is make the phone boot from the boot server and it will automatically update its firmware.
There are two methods to get the phone to use the boot server; Method 1 is to enter the address of the boot server into the phone using the keypad. This has the benefit of simplicity. Method 2 is to program your DHCP server to tell the phone the boot server address. This has the benefit of ultimate simplicity, since all you have to do is plug the phone in to make it work, but at the expense of the hassle of setting up the DHCP server: