I am letting my users select files from the music library. After which I am storing the path of the selected files locally. Now my problem is how do I get access to the file
You will want to use the access cache to store access to the files instead of the paths. This will let you retrieve StorageFile objects that you can work with right away, and will help with some scenarios surrounding files being moved.
To store a file in the access cache
StorageFile file; //Get a file
string mruToken = Windows.Storage.AccessCache.StorageApplicationPermissions.MostRecentlyUsedList.Add(file, "20120716");
You then save the token some where. To get the file back from the cache:
StorageFile file = await Windows.Storage.AccessCache.StorageApplicationPermissions.MostRecentlyUsedList.getFileAsync(mruToken);
Storing just the path opens you up to issues with drive letters changing ect. This ensures that if the file is still available, your app can get it.