How would one make an extremely quick/low latency/fast/etc. echo server?

1) get copy of Linux kernel source
2) make changes to TCP/IP stack to do the necessary work as soon as you receive the network packets
3) install newly-changed kernel on Echo server

any computer is already capable of responding to an echo faster than it's network card can transmit again using the normal manner, without kernel tweaks.

If you assume "echo" to mean "ICMP ECHO" then C-junkie is correct: the kernel work has already been done for you. I was assuming another meaning of "echo server". If you give more details, RolandofGilead, then I think we can give better answers.

the echo server would be in charge of receiving and sending data to and from the outside network and another socket program