Even if you do own the site, you should take a good STRONG look at the TOS of whatever ISP you will be going through. Most ISPs that provide home service*, do not allow you to do things like port scans over the WAN. In fact, a lot of the ports may be closed. The ISP of the server site may also have objections to you doing this, and you will likely need written clearance from both.
After you clear those hurdles, the answer to "how to go about this?" is "It depends." There isn't a cookbook to Pen Testing. I would suggest download and read the OSSTMM. It should give you some insight on the methodology.
*This is assuming for the moment that you'd be attempting to pen test this server from your home. The amount of inexperience reflected in the question is pretty apparent. Otherwise you'd know how to go about this, and already know about things like TOS restrictions.



