Solved it. For anyone else who hasn't found the documentation for it, here is the answer:

For this example, the main page is called NewCustomer.aspx.  Input fields have been added to an asp UpdatePanel named ClientInfo (ClientInfo.ascx) that is part of the NewCustomer.aspx page. There are three types of input fields that have been added to this page -- a straight text input box, ID "BirthCity", a dropdown selection box with the ID "BirthCountry" and input box named 'DOB" which is using jQuery Datepicker calendar to select the date.

The following metafields were created in CommerceManager and added to the OrderForm (OrderFormEx): CityOfBirth - Short String, CountryOfBirth - Short String, IDDOB - Short String.

This code is added to the code behind (ClientInfo.ascx.cs).

===========================================

public OrderForm CaptureMetaFields

{
    get
    {
        var orderForm = new OrderForm();

        if (BirthCity.Value != null)
            orderForm["CityOfBirth"] = BirthCity.Value;
        if (BirthCountry.SelectedItem != null)
            orderForm["CountryOfBirth"] = BirthCountry.SelectedItem.Text;
        if (DOB.Text != null)
            orderForm["IDDOB"] = DOB.Text;

        return orderForm;
    }
}

=====================================

NOTE: There is a "get".  There is no "set".

This code was added to code behind for NewCustomer (NewCustomer.aspx.cs) 

=====================================

// Insert OrderForm MetaFields
var orderFormId = ClientInfo.CaptureMetaInfo;
purchaseOrder.OrderForms[0]["CityOfBirth"] = orderFormId["CityOfBirth"];
purchaseOrder.OrderForms[0]["CountryOfBirth"] = orderFormId["CountryOfBirth"];
purchaseOrder.OrderForms[0]["IDDOB"] = orderFormId["IDDOB"];

purchaseOrder.AcceptChanges();

========================================

These two steps populated the fields in the database table OrderFormEx.