Accessing the value of a field on a SUBFORM is tricky. Normally, getting a value off just one form is:

=Forms!FormNameF!FieldName

If you're dealing with a SUBFORM then it becomes:

=Forms!FormNameF!SubFormName.Form!FieldName

You can put this value in the Default Value property of your new form, OR it might be easier to go the other way. In the VBA code for the button that opens this new form, you might just want to set the value manually in the new form after opening it.

DoCmd.OpenForm "NewFormNameF"
Forms!NewFormNameF!FieldName = SomeValueOrField

If the button is IN the subform of which you speak, then you wouldn't need to use any crazy notation. I cover this when we get into the 300-level series of Access courses and start learning VBA.