Ironically, It's The Eastern Section Of The US Writers' Guild Doing The Interviewing

I'm currently watching my way through all of The West Wing, and in general it's very good indeed*.

Much of the credit for this, obviously, has to go to writer-creator Aaron Sorkin, and I thought it was worth me pointing you to this link, a 2003 Writer's Guild of America publication featuring a ten-page interview with Mr S, followed by a copy of the pilot script for The West Wing.

By way of taking a look behind the curtain to see how it's done, I'd say it's worth your time.

*I haven't got to the post-Sorkin era yet, so can't voice an opinion on the reported dip in quality once he's gone (though I gather it finds its feet again after a bit).