You can't add it to the list from within the Fie class - it doesn't (and definitely shouldn't) know even of the existence of the List of Fie instances so it can't access it in any way.
To add a new instance of Fie to your list is simple:
public class Record
{
public List<Fie> Field = new List<Fie>();
void AddIt(string s)
{
Field.Add(new Fie(s));
}
}
But it is also considered poor practice to publicly expose your fields directly - you should use a property instead (and possibly return a copy of the list instead of the actual list itself).