How to use my own web hosting server to mine a bitcoin?
It's as simple as sshing into your server and installing a bitcoin miner such as this one. A server is just a computer and a bitcoin miner is just a program so as long as you can install programs via a terminal you should have no problem and any old getting stated bitcoin mining guide should work.

That being said, this is generally not a good idea to do. Bitcoin mining has gotten to the point where to be cost effective you have to use custom built chips. This means that if you mine bitcoins on a regular old web server making use of the CPU or even the GPU, you will loose money on electricity + server costs. 

If you truly do have unlimited free webserver time, then hell, go for it, but understand that this is a net capital loss, your just externalizing the cost to your server provider.