First off, don't try to to it in the form you display when they select "New" - that form should know nothing about how you display the data it collects. Instead, treat the "New" form in the same way that you do a OpenFileDialog form: create it, set up it's parameters, display it, and then use the properties to tell you what the user did.
MyNewItemForm myForm = new MyNewItemForm()
if (myForm.ShowDialog() == DialogResult.OK)
{
string item = myForm.NewDataEnteredByTheUser;
TreeNode t = new TreeNode(item);
myExistingNode.Nodes.Add(t);
}