Download Your GTFS Feed
Locate your feed's posted location. Trillium posts all feeds at a static download location, and encourage the same for all agencies to allow for developers to access the data. Contact email@example.com if you are unsure of the location of your feed.
Import Your GTFS Feed
Convert GTFS to KML
KML is a file format that is readable by many programs, including ArcGIS and Google Earth. If familiar with Python, use the open-source script kmlwriter.py. The resulting KML file shows Stops and Route Alignments.
Convert GTFS to GIS Shapefiles
Instructions for this approach, and other methods, are here on Steven Vance's blog.
Note: this article is now several years old, so there may be some changes to the process documented here. Please provide notes on your experience.
Import GTFS into the ArcGIS Network Analyst Tool
Melinda Morang describes this, and more, on the site Using GTFS Data in ArcGIS Network Analyst.