Let's split it out...
In a pitched battle:
Flying wyverns are useful, but not necessarily game changing. I'm assuming that wyverns flame breath is going to be short range, at least compared to an arrow. Wyvern wings are big and exposed. Against a prepared group of bowmen, wyverns become target practice.
You don't need any fancy weapons to kill them. A standard longbow is already designed for range and power - it could easily punch a hole through a wyvern's wing membrane. All it would take is a couple of good shots and the wyverns will fall hard.
In terms of ballista, instead of scorpions or catapults there would be a greater emphasis on 'scattershot' weapons. Wyverns are highly mobile, so you need to launch a wide area of debris in order to take them down.
There would be organised volleys of projectiles whenever the wyverns are in range, as well as dedicated anti-wyvern archers. It should be noted that wyverns are distinctly unarmored, so taking them down is not that difficult.
The best use of wyverns in that case is to give the riders bows themselves. The wyverns fly safely out of bow range, and their riders take free shots at an army below. They'd have awful accuracy, but who cares?
Of course, this assumes that the enemy is prepared. If the enemy is unprepared, the wyverns become much more useful. If the wyverns dive and the bowmen aren't ready for them, then shock and awe alone would have a huge effect.
If the battle is already won and the enemy if being routed, the wyverns become free to swoop down and inflict maximum damage. It would be the demotivating finishing blow to end a battle.
In a siege:
If sieging a castle, wyverns are a bit more useful, but they still can't replace a standard army. Wyverns still lose against bowmen, so they can't assault a fortress themselves.
But the point in siege is that the defenders can't maintain a full guard all the time. Sooner or later the defenders will slack, and then the wyverns shine. Wyverns could very quickly lift a ladder over the walls, or drop a group of assassins on the roof, or set a stable on fire in the courtyard.
It becomes much more difficult to defend against against flying foes. Wyverns would be great for constantly harassing a group of stationary defenders trapped in a castle.
In skirmishes / raids:
Now, this is where the wyverns become the most useful. Wyverns move quickly, and they can terrorise an undefended populace. The wyverns can fly over the countryside, burning farms, and hurting the enemy where they're most vulnerable - their infrastructure.
The enemy will send groups of mounted archers to hunt the wyverns, but the flying raiders will just fly away and attack elsewhere. The wyverns have the advantage of absolute mobility, they should use that.
Sooner or later, when the people realize that their government can't protect them from these flying raiders, it'll spark riots against the government.
Of course, all this assumes that you have wyvern riders and there enemy does not. In practice, as soon as one nation tames wyverns, the other nations will work very hard to tame their own wyvern. From then onwards, in warfare, the two opposing forces of wyvern riders will be too busy fighting each other to harass the ground.
It would be rather like the role of aircraft in World War I; the aircraft themselves are flimsy, and the air forces spend their time fighting each other, while the ground forces are fighting below. The contest for sky superiority almost becomes a separate battlefield.
In reconnaissance:
Honestly, this is where the wyverns would be absolutely essential. I'm assuming you probably don't have many tamed wyverns, and it would take a large investment to rear each one. For the most part, the wyverns are likely going to be too valuable to risk in battle, and would be resigned to the 'boring' jobs.
Instead, most wyverns would be dedicated towards scouting, navigation and ferrying messages. It should be noted that medieval armies largely sucked at information chains. Forward scouting was poor, sending messages was a risky business, and men on foot took so long. Many early commanders were loathe to ever split their armies because they knew they wouldn't be able to coordinate afterwards. Rather than enacting any complicated tactics, most medieval armies just blundered their way through.
The wyvern riders would change that. I'd expect each wyvern to be ridden by a very distinguished noble knight, someone trusted to pass on orders and to represent the king himself. For the most part, the wyverns will avoid combat, but felling even a single wyvern and its rider would mark a major achievement for the enemy.
