Wikipedia:Policies and guidelines describes how Wikipedia arrives at its policies and guidelines through a process of discussion and consensus. Discussion takes place in the various policy pages which form part of the "Wikipedia:" namespace. Sometimes policy is discussed off-wiki, but decisions always take place on-wiki.
Two words for the same thing. An administrator is simply a volunteer Wikipedian who can access some of the few restricted Wikipedia software functions: deleting articles and files, protecting and unprotecting pages, and blocking and unblocking users. The software internally uses the string "sysop" to flag their accounts, a shortened term for system operator. See the current list of administrators.
You must have years of a good edit history that shows you understand Wikipedia policies, have good judgement, a good temperament, and have a need for the administrator toolset. A nomination is then made at Wikipedia:Requests for adminship where the community decides if the user deserves the tools. Honestly, you can do 95% of tasks on Wikipedia without being an administrator.