Where there is a group of people, there will be politics and organizational dynamics. This should be no different with the Sangha.
For example, monks trying to cause dissent or schism, monks who disobey instructions, monks trying to gain power over others, monks who are envious of others, monks trying to get the attention of the Buddha or their abbot etc.
How did the Buddha handle such situations in his time?
How are such situations handled within the Sangha today?
How did the Buddha handle such situations in his time?
There are two famous schisms in the time of the Buddha; the Devadatta schism and the Kosambi schism.
In the former case, new, inexperienced monks were led astray by bogus teachings and the Buddha sent his two chief disciples to explain the truth to them.
In the latter case, the Buddha tried to invoke the seventh means of settling disputes (adhikaranasamatha), called "covering over with grass" - i.e. agreeing to leave the past transgressions behind and start fresh. The monks refused and the Buddha abandoned them.
To some extent, it's not very instructive to ask "how did the Buddha handle X", since he was fully enlightened and knew how to best deal with every specific situation. Better to ask is how the Buddha taught one should deal with sangha politics. In this instance, he left fairly specific procedural teachings on how to avoid and deal with such affairs.
Briefly, the seven adhkaranasamatha for dealing with disputes and legal cases are:
Beyond this, there is specific and lengthy instruction in the vinaya regarding schisms, and there are various teachings on dealing with power struggles, envy, disobedience, etc.
How are such situations handled within the Sangha today?
Rather poorly, for the most part. But "the sangha" is a huge and diverse conceptual body that for all intents and purposes doesn't exist as a single entity. Various sects, traditions, and even countries have their own sanghas now, and each sangha has its own means of dealing (or not) with such problems. For the most part, it is far more difficult to actually deal with monastic transgressions in modern times; without the stability of a large body of enlightened beings, it's much more "every monk for himself", unfortunately.
The nature of our present time is very different from Buddha's time: after the printing press "politics" really started taking on an industrial and corporate mission.
On the other hand, the ruling monastic order, the Vinaya in particular was passed on entirely orally. This should answer your first question. Any question on how Buddha handled X, can be answered in the Vinaya. In my opinion, it is frequently contextual and oftentimes impractical for our times.
We live a different day today: a day of bodhisattvas and renaissance men.
As for specific cases of "politics" which didn't really exist on such an organized level for lack of printing press, there is the case of Devadatta taking over the initial political expression of Buddhism. (Osamu Tezuka's Buddha manga beautifully renders this story.)
Eventually Devadatta tried to kill Buddha, too, symbolizing the message from Buddhism about poltiics: "power corrupts."
Even more broadly, contrived action corrupts, especially socially contrived action tends to create backlashes within and without. We are one collective organism and when good is born, evil persistently tries to take over, day and night. When there is no contrived good, there is no contrived evil.
This is why Buddhism and Taoism philosophy are often very close, with Taoism taking an even more non-interfering attitude towards things, having the overall expression of "let all karma go up and down, when everyone tires of controlling and contriving, they will rest within the natural order."
The Buddha himself didn't do much in terms of managing the Sangha, just like any of the Zen masters (who are even more strict, some forbidding writing or taking notes). Even when he passed on leadership to Mahakashyapa, all he did was raise a flower and smile (likely paranormal methods of transference involved).
How is politics active in Buddhism today? Highly active! There is SGI international, Tibetan Buddhism affecting politics in China, and with the marriage of Buddhism and scientific brain analyses, an overall recognition of the importance of samatha and vipassana meditation for happiness and maturity.
I think we have reached an excellent point today and there are many different "politics" with simple rules in smaller meditation circles to clear echelons of managerial staff, teachers, web developers, etc. for mini Buddhist societies. It certainly doesn't seem like the Buddhadharma (whether in the form of Buddhism or other traditions which focus on Insight Meditation) is nearing any sort of Dharma Extinction Age (where it is said that people will be reading and studying but few will have any Realization).
