Probably the easiest and fastest way to determine the showrunner of a given series is to simply google the show title and the word "showrunner". The entertainment press always uses the term these days, so it's easy to find who is the person who's responsible for the overall direction/tone/message of the show.
The showrunner is always credited as an Executive Producer, and will typically have the "Created by" or "Developed by" credit as well, but not always. Sometimes the show was handed over to a different showrunner (e.g., Dead Like Me, which was created by Bryan Fuller, but which was eventually showrun by John Masius; or Revenge, which was created by and initially showrun by Mike Kelly, but after the second season, was handed over to Sunil Nayar). The showrunner generally has the final Executive Producer(s) credit immediately before the individual episode writer and director credits.
As with film credits (at least in the USA--it doesn't necessarily hold for UK television), the ampersand (&) indicates collaboration, while the word "and" indicates a rewrite (with the order of the names giving the order of drafts; i.e., the first name did the first version; the second name did a rewrite). So, if the "Created by" credit has two names with an ampersand between them, the show is being team run. If the "Created by" credit has two or more names separated with "and"s, then it's likely the last name (or group of &-separated names) is the showrunner.
All showrunners write for the show, some direct--but not all, so following those credits may or may not help. But most typically, the showrunner(s) will write the pilot and/or finale episodes of a season.