They will send you to the ticketing office for three possibilities:
1) upgrade your fare to business class (provided fare rules of the original ticket allow that)
2) upgrade your fare to fare class B with a fixed fee per fare class AND pay mileage to upgrade to business cabin (not for V-class, not for AF flights)
3) upgrade with miles to business cabin (S/B fare code only on KL)
--> 1) possible if seats for sale in availability display 2/3) possible if any spare seats in the flight load but subject to approval of flight supervisor.

Alternatively you can swipe your credit card onboard for an onboard upgrade.
But note that comes at a very hefty fee (usually much more expensive than option 1)