To do this manually, you’d need something like:
List<string> existing;
if (!myDic.TryGetValue(key, out existing)) {
existing = new List<string>();
myDic[key] = existing;
}
// At this point we know that "existing" refers to the relevant list in the
// dictionary, one way or another.
existing.Add(extraValue);
However, in many cases LINQ can make this trivial using ToLookup. For example, consider a List<Person> which you want to transform into a dictionary of “surname” to “first names for that surname”. You could use:
var namesBySurname = people.ToLookup(person => person.Surname,
person => person.FirstName);