The Jedi operate primarily out of the Grand Temple on Yavin IV, lead by a council of the most respected Jedi Masters, headed by Grandmaster Luke Skywalker. Jedi have a great deal of independence to operate on thier own, although the organization itself is a member state of the New Republic. Masters, Knights, and Padawans tend to travel freely to and from the Temple on thier own investigations and journeys with barely a degree of coordination with the main temple, reporting in as warranted. Virtually the only thing that is centralized is the main training of younger students at the Temple, which is considered more a matter of building community bonds than training necessity; many Jedi almost never go back to the Temple nor coordinate with it after they finish basic training.
Training for younglings and adult recruits is focused on teaching basic control and awareness of the Force, and it is common for them to then be put in groups with an independent master who trains them personally and takes them into the field. The Jedi of today are far more open to differing interpretations and traditions of the Force than those of the past, including interpersonal relationships. This has lead to degrees of friction and multiple schools emerging within the Order, but ultimately they seek the same end - harmony in the galaxy and spiritual enlightenment.