I've always been under the impression that the main effort was undertaken by the Royal Navy, but have recently been trying to find out more on the involvement from the RAF.
How important was the bombing of Stanley airfield by the Vulcan (and Harriers?)
Did the RAF contribute much to air superiority or was this achieved by the Sea Barriers of the FAA?
In terms of fighting, the role of the RAF was virtually nil. The vulcan runs on Port Stanley cratered the airfield but it didn't stop its use by pucara ground attack aircraft, and iirc didn't stop its use by hercules either.
The simple reason the RAF played little part in the fighting is that the Falkland Islands were too far away from any British airbase. The vulcans were only able to reach the islands after an epic journey taking them well outside of their usual operational range.
Probably the RAF's main contribution to the war was logistical - flying men and materiel in and out of Ascension island, the staging post for the fleet. Some RAF harriers were also transferred to the fleet, but I assume these were operated by the navy, as RAF crews wouldn't be trained for the role.
(As usual, main source for this is The Battle for the Falklands by Max Hastings and Simon Jenkins.)