The Magisterium is the Teaching Authority of the Church.
It promises that the Holy Spirit is at work in all members of the Church and so it will never go astray, even if the people do.
The Magesterium have to understand the passages in the Bible and apply them to modern day life so we can understand it. Except, they never introduce a new announcement quickly or accept quickly.
This is because they believe it is valid if it withstands the 'test of time' and is universally accepted. They fear that if they release something too quickly and make a mistake, people might stop believing the real truths.
So the Magestriums methods are slow but infalliable (cannot be wrong).
The Pope is centeral of the Magisterium. Peter was Bishop of Rome and died in 67AD, since then there has been an unbroken succession of him. They convey the same faith as the apostles. They are based in Vactican City in which is St. Peters Basilica which is built on top of his tomb. This refers to when Jesus called Peter 'rock' of which he could build his Church. The Church is also infalliable so when the Pope speaks Excathedra, he is infalliable too. The Pope issues encyclicals which are documents dealing with the matters of the time but these are not infalliable but offer guidance and support.
When a Pope dies, the cardinals gather in a conclave (isolated with only one assistant) to ballot a new Pope. Before, they ask for the inspiration of the Holy Spirit which will encourgae them to pick who God wants. To win the election, you need to have 2/3 plus 1 of the votes to prove the full support.
The Pope and the Bishops
As the Pope is a successor of Peter, the Bishops are successors of the apostles. They are also the head of the local Church.
Their role is to advise the Pope and teach faith. They also organise the Parishes, ordaining of preists and the rite of confirmation. He sends out pastoral letters to parishes, giving information and guidance.
They are appointed by the Pope and consult him with affairs from the diocese (the area selected for him). The central Church building of a diocese is called a Cathedral and the focal point is the Bishops chair (Cathedra).
A General Council is when all Bishops are summoned by the Pope. They discuss Church affairs and the last Council was 1962-1965. The effect of this was the change of the language of the Mass from Latin to English. Even though they can voice their opinions in the Council, the Pope has the final say.