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.