Information about the Middle Ages:

https://en.wikipedia.org/wiki/Middle_Ages

Many fantasy stories takes place within the medieval period of time. However, there is misconceptions about it. Let me break it down for you.

First, the people would call it "the Ages" unless specifically called something else by the denizens. And the time period is often broken down into three parts by historians.

The Early Middle age, the first part. It is when you often have the rise of individual kingdoms. Religions are established. And it is the rise of mail armor and longswords. The plate armor does not exist in this time. Longswords are carried with both hands. 

https://en.wikipedia.org/wiki/Longsword

Mounted infantry exists. Early stirrups and horse shoes is made to help horses to move and then go on rocky terrain. They are effective against soldiers. My counter idea is using wooden poles cut to have points aimed towards the riders. Horses will not ride into objects and people.

This age is where local governments formed and the most conflict happens in the local areas. Do not expect thousands to flock to a cause. Individual interests plays a lot in this time period.

High Middle, or Mid Middle age, the second and middle part of the three. Established states and kingdoms taken hold. Construction of castles taking root and leading to large stone buildings. Alliances and marriage deals is important to the rulers. Larger armies than the Early Middle age due to success of farm technologies. Horse ploughs are in use as well as dividing lands and rotating crops.

Cavalries are well trained and have horse armor. Closed face helmets exists with heavier armor. Chest plates exists. There is crossbows which is a important defensive tool. Defenders of castle will have them. The smart attacker will not engage a castle at the gates unless they need to.

Why? Answer: Canons

Breaking down walls with cannon fire is important. Gunpowder is made. Although not highly weaponized, the cannons is the sieger's best tool.

Question: can we have a story without cannons? 

Answer: I guess so. But how are those wall broken down? Magic comes to mind. 

Another, is the employment of sappers digging underneath and blowing the walls from below. Of course it takes days to weeks.

If there is a will, there is a way. Be creative and explain how those walls going to be broken down. If those walls cannot be broken, then every castle becomes a death trap to attackers. And a form of stalemate happens and every kingdom can't be conquered and allow the next period to take place.

I will talk about it in the next chapter.