GTFS data contains stop locations, schedules, route alignments, service calendar, and fares. The data that it contains can be imported into other applications, including software such as ArcGIS or QGIS, for analysis. This article contains instructions on how to import GTFS data (see also General Transit Feed Specification reference).
Step 2: Import the data. Depending on your needs, choose one of these import methods for ArcGIS.
A.) Convert GTFS data to a KML (Google Earth) file that can then be imported into ArcGIS.
Use the free, open-source python script kmlwriter.py to do this. The resulting KML file shows stop locations and route alignments.
B.) Import the GTFS shapes.txt file directly to ArcGIS. Instructions for this approach, and other methods, are here on Steven Vance's blog. (Note: this article is now 4 years old, so there may be some changes to the process documented here. Please provide notes on your experience.)
C.) Import GTFS into the ArcGIS Network Analyst tool. Melinda Morang describes this, and more, on the site Using GTFS Data in ArcGIS Network Analyst.