How to find who is the showrunner?

I don't believe that there's a standard way as they are not credited as such. Showrunners are always credited as Executive Producers. Additionally, they also usually receive credits as a Creator, Writer, and/or a Director. They are all inevitably writers.

Looking up IMDb's crew list for:

• Mad Men suggests that Matthew Weiner is the showrunner
• Star Trek: Enterprise suggests that Rick Berman and Brannon Braga were joint showrunners
• Doctor Who suggests that Russell T. Davies was the showrunner until 2010 after which Steven Moffat took over; Julie Gardner was also the executive producer with Davies, but she didn't have his writing credits.

(I haven't watched any of the above shows.)

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). With US half-hour comedies, the showrunner(s) typically have the first executive producer credits, as producer credits go in hierarchy order. With US hour-long dramas, the showrunner(s) generally has the final Executive Producer(s) credit immediately before the individual episode writer and director credits, as producer credits go in reverse hierarchy order. Although, with Evil, I did see the showrunners' credit card delayed to be the first of the end credits.

As with film credits (at least in the USA with live action—where the WGA determines credits), 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.

re: 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" & "most typically, the showrunner(s) will write the pilot and/or finale episodes of a season":

It seems most likely to be a writing credit. For example, for the original TV Batman, Lorenzo Semple, Jr would have been showrunnner with the title Executive Story Editor. He wrote only the first four episodes, but served as a script or story consultant on every other installment. He also penned the show’s “bible” for the other writers.

There must have always been showrunners but it only surfaced as a term in recent years. Did the classic 50's, 60's, 70s show have them? They didn't get publicized as such.

Surprised the Writers Guild doesn't have some standardized terminology for showrunner.

The showrunner is the person the studio looks to to make sure there's a script for every episode. There wasn't one, for the 13th episode of Robbery Homicide Division becomes the showrunner, Frank Spotnitz, left and Michael Mann was too busy getting his next picture started to take over the writing at that level of focus.

The showrunner gets the scripts written effectively. He runs the writing room. He solves the story problems. He/she may start as a writer, become a co-ordinating producer, then a executive producer. And you'll see scripts written by that person. Leonard Goldberg, a very good producer, is the last Executive Producer credit on Blue Bloods, but he's not the showrunner. Someone else is responsible for that job, under Mr. Goldberg's aegis. Sometimes you just have to look it up: the credits are not helpful but by inference here. But they are all in the Writer's Guild. They started as writers, demonstrated ability to turn in good scripts on time for many years, usually. So, yes, show runners are writers in the writers guild. They also usually producers, for the credit, $ & authority. Look at IMDB, see who the writers were. The show runner is in that list, always.