The peacekeepers of the galaxy, the monastic Jedi Order has served in their role for Centuries. Through observation of the Light Side of the Force, the Jedi try and preserve peace and justice. Of course they also strive to balance out the Dark Side of the Force and its' worshipers, namely the Sith.
The Jedi High Council is the central, organizing for Jedi throughout the galaxy. Located on Coruscant, the council serves as not only a governing body for the order, but also a center of knowledge and teaching. Here new Jedi are taught use of the force, self defense, use of the Jedi's signature weapon the Lightsaber, and of course the Jedi Code. It is on Coruscant that the council also meets with the leaders of the Republic to discuss ways the order can best help promote peace throughout the member worlds.
That said, there are many other Jedi Temples and Academy's throughout the galaxy. While the council is the main authority of the Jedi Order, there are many interpretations of the Jedi Code and how to best observe the Light Side of the Force. It's not uncommon to find a Jedi Master who vehemently disagrees with the Jedi High Council and simply ignores it. In the aftermath of the Great Sith War many enclaves and academies broke contact with the Jedi Council to follow their own paths and teach their own interpretations. The Jedi High Council is attempting to reassert its authority, and hold Jedi Masters and Jedi Watchmen to higher standards, but this is a long uphill battle.
Force sensitive beings from across the galaxy are chosen at an early age to become students of the Jedi Order. They train for years in how to use the force, defensive arts including lightsaber combat, and of course in the Jedi Code. Eventually this young Jedi is selected to become a Jedi Padawan.
Padawan are selected by more experienced Jedi to become an apprentice. Following the direct teachings of their master, the young padawan learn first hand what it means to be a Jedi in the world outside the academies. When their master feels they are ready, they will be taught the final secrets of the Order, including building one's own lightsaber. The young padawan can then be brought before a Council of Masters who will determine if he is ready to be given the title of Jedi Knight.
Knights are fully fledged Jedi. They are able to venture into the galaxy on their own, conducting missions as they see fit though most still take on missions provided by the Jedi Council. Knights can also chose to take on a padawan learner as an apprentice. It is though oversight of a successful transition of padawan to knight, that a knight can become a Jedi Master.
Masters have much more autonomy than knights. Masters can still teach padawan learners, but they may also teach and find those worthy of joining the order. Some serve in the academy they learned from, while others go as far as opening their own academies. While a Master is the highest title one can archive in the order, there are two other higher positions a master can receive.
- Jedi Watchman - Watchmen are chosen to watch over and protect particular planets in the galaxy. The are also the ones who seek out force users among the populace and determine if would be a good candidate for the Order.
- Councilman - Jedi Councils are the ruling body of the order. While the Jedi High Council on Coruscant is highest level of oversight, most temples and academies keep their own council to oversee the day to day operations.
The founding of the Jedi Order predates the Republic by centuries. The exact details of founding have been lost over time, but all agree that it was a gathering of philosophers, priests, scientist and warriors who created the first principals of the Jedi including the Code.