When booking economy and seats in first class or business class cabins become available, you can ask the cabin crew to upgrade you from economy to Swiss business class or first class on my flight for free if you want special assistance. If you're on a particular vacation or a frequent traveller, use your title. They might be able to assist you in the same way.
When you're on a flight and seats in first or business class become available, an announcement may be made offering seat upgrades for a fee of $500-600 for upgrading from economy to business class and roughly $2000 for moving from business to first class.