// Incomplete code snippet assumes variable Item item with list field "References" and IEnumerable<ID> references

Sitecore.Text.ListString referencesValue = new Sitecore.Text.ListString();

foreach(ID id in references)
{
   string idString = id.ToString();
   if (!referencesValue.Contains(idString))
   {
       referencesValue.Add(idString);
   }
}

item.Editing.BeginEdit();
item["References"] = referencesValue.ToString();
item.Editing.EndEdit();