From an answer posted here: http://stackoverflow.com/a/20559175 converted to Xamarin.Android

DocumentHelper.cs

public static class DocumentHelper {
	public static string GetPathToFile(Context context, Android.Net.Uri uri) {
	    bool isKitkat = Build.VERSION.SdkInt >= BuildVersionCodes.Kitkat;
	
	    if (isKitkat && DocumentsContract.IsDocumentUri(context, uri)) {
	        if (uri.IsExternalStorageDocument()) {
	            var parts = DocumentsContract.GetDocumentId(uri).Split(':'); 
	            var type = parts[0];
	            var name = parts[1];
	
	            if (type.Equals("primary", StringComparison.InvariantCultureIgnoreCase)) {
	                return string.Join("/", Android.OS.Environment.ExternalStorageDirectory.AbsolutePath, name);
	            }
	        } else if (uri.IsDownloadsDocument()) {
	            var id = DocumentsContract.GetDocumentId(uri);
	            var contentUri = ContentUris.WithAppendedId(Android.Net.Uri.Parse("content://downloads/public_downloads"), long.Parse(id));
	            return GetDataColumn(context, contentUri, null, null);
	        } else if (uri.IsMediaDocument()) {
	            var parts = DocumentsContract.GetDocumentId(uri).Split(':');
	            var type = parts[0];
	            var name = parts[1];
	
	            Android.Net.Uri contentUri = GetContentUri(type);
	            var selection = "_id=?";
	            var selectionArgs = new string[] { name };
	
	            return GetDataColumn(context, contentUri, selection, selectionArgs) ?? string.Empty;
	        }
	    } else if (uri.Scheme.Equals("content", StringComparison.InvariantCultureIgnoreCase)) {
	        return GetDataColumn(context, uri, null, null) ?? string.Empty;
	    } else if (uri.Scheme.Equals("file", StringComparison.InvariantCultureIgnoreCase)) {
	        return uri.Path;
	    }
	
	    return string.Empty;
	}
	
	private static Android.Net.Uri GetContentUri(string type) {
	    switch (type) {
	    case "image":
	        return MediaStore.Images.Media.ExternalContentUri;
	    case "video":
	        return MediaStore.Video.Media.ExternalContentUri;
	    case "audio":
	        return MediaStore.Audio.Media.ExternalContentUri;
	    default:
	        return null;
	    }
	}
	
	private static string GetDataColumn(Context context, Android.Net.Uri uri, string selection, string[] selectionArgs) {
	    var column = "_data";
	    var projection = new string[] { column };
	    using (var cursor = context.ContentResolver.Query(uri, projection, selection, selectionArgs, null)) {
	        if (cursor != null && cursor.MoveToFirst()) {
	            return cursor.GetString(cursor.GetColumnIndexOrThrow(column));
	        }
	    }
	
	    return null;
	}
	
	public static bool IsExternalStorageDocument(this Android.Net.Uri uri) {
	    return uri.Authority == "com.android.externalstorage.documents";
	}
	
	public static bool IsDownloadsDocument(this Android.Net.Uri uri) {
	    return uri.Authority == "com.android.providers.downloads.documents";
	}
	
	public static bool IsMediaDocument(this Android.Net.Uri uri) {
	    return uri.Authority == "com.android.providers.media.documents";
	}
}