When you open "View|Header and Footer" a toolbar should pop up. 1. At the right end it will say "Close" 2. Next left of that will be a "page" with a bar at the top and a right pointing arrow at the bottom. This one goes to the "next header/footer." 3. Next left of that will be a "page" with a bar at the top and a left pointing arrow at the bottom. This one goes to the "previous header/footer" 4. Next left of that is a "page" with bars top and bottom. This toggles between header and footer.
5. Next left of that is a "two pages with a dashed arrow going from the one on the right to the one on the left." If you hover over it (if you have "tips" turned on) it will say "Same as Previous." THIS IS THE ONE YOU WANT.
It will be "grayed out" while you're in the first section.
When you Insert|Break|Next Page, the status bar should show that you're in "Section 2." If you open the View|Header and Footer, the toolbar will have the "Same as Previous" Icon "lit up" to indicate a "depressed button." Click it once to turn it off, and when you insert the header for the second section the header in the first section should remain unchanged.
(It should work quite simply when you're putting in new sections, but can be a real p.i.a. if you need to delete a section that comes between two other sections with different headers. That's in the advanced class.)