Luke Skywalker founded the New Jedi Order from the ashes of the previously demolished Jedi Order, which was obliterated by Emperor Palpatine, Darth Vader, and the Galactic Empire. After the war was finished, Luke met other Jedi and Force sensitives, and he later recruited them to join his new Order.
The New Jedi Order utilized many bases in its time. The most notable, however, would be the following:
The Jedi Praxeum on Yavin IV
This was the first HQ used by Luke early on in the new Order's history. There, he trained many students of various ages in the ways of the Jedi. Among the teachers there would include masters Tionne and Kyle Katarn. The Jedi Academy would remain one of the New Jedi Order's primary training facilities until it was destroyed by the Yuuzhan Vong, who transformed it and the area around it to suit their needs.
Jedi Headquarters and Rebuilt Temple on Coruscant
The Jedi utilized a base on the ruins of the old Jedi Temple, which was almost completely decimated during Operation: Knightfall - the assault on the Temple led by Darth Vader. Many years later, after the retaking of Coruscant from the Yuuzhan Vong, the Jedi Temple was rebuilt.
Jedi Academy on Ossus
Ossus was one of the main headquarters of the Jedi Order thousands of years prior, before it was almost destroyed in a plot by Exar Kun. The planet held many artifacts, which were recovered by Luke Skywalker and his students, who created a new base there. This was the main headquarters of the New Jedi Order for decades before it was invaded by the One Sith about a hundred years later, effectively destroying all of what Luke tried to accomplish.
The Hidden Temple
The Hidden Temple on Taivas served as a hiding place for the New Jedi Order and the Jedi Council after the conquest of the One Sith, forcing the remaining Jedi into exile.
Belief Differences from the original Jedi Order
Luke Skywalker made many radical changes to the Jedi's belief system that was used by the Jedi Order of his father's time.
Luke's Order never denied anybody training in the Force, regardless of their age. The previous system usually only admitted infants. Luke's Order often took in full-grown adults.
Emotional Attachment and Marriage
Unlike the previous Jedi Order, Luke's order did not forbid emotional attachment, including love or marriage. Many Jedi under Luke's Order married, including the Grandmaster himself, and had children. This would also include Leia Organa Solo, Corran Horn, and other Jedi. Many Jedi also kept close with their family. They also had family training family, such as when Jacen Solo was the master to his nephew, Ben Skywalker.