This blog post by webrian explains how to use OpenStreetMap data in GRASS GIS. This in detail description uses GRASS commands as v.net.path, v.clean and v.distance and many more. This is a very old post, so probably there are many more and different (and probably more efficient) ways to perform routing tasks within GRASS GIS, especially regarding the new capabilities of GRASS 7 which is available e.g. as beta version. However, any routing needs a proper data base which involves routeable, non-erreronous e.g. street networks like data provided by the OpenStreetMap project. There are many ways to download data from OpenStreetMap as described here. For example, the geofabrik offers different products and maps e.g. from Germany to download: http://download.geofabrik.de
here the original blog post: webrian: Routing with OpenStreetMap data in GRASS GIS.