I'm planning to use Open street map in my Rails app to track locations, Can any one guide how to integrate Open street map with Rails 3.2, using MongoDB.
Sadly I'm not experienced with Rails, but will try to answer:
If you just want to display OSM as basemap and add custom vector geoinformations on top, you will like to consider Leaflet or OpenLayers to display the informations that are streamed via GeoJSON/WFS/... and use a Rails geospatial framework to process and serve your data in this formats. MapFish seems to have also a rails plugin.
If you want instead process OSM geodata itself via Ruby, there are libs for accessing the main API (please not use for bulk data download) and work with the data:
What you usually not want is to build your app on top of the Rails port, that runs the osm.org website, OSM API, ... .
Hope that was hopefull or could at least give you an idea about where you want to go :)