Politics is the practice of managing the internal and external affairs of a political entity. Those who practice in political roles and duties are known as politicians or statesmen.
Klingon and Cardassian politics have been described as being both "very complex" and "intricate". (TNG: "Reunion"; DS9: "Ties of Blood and Water" The Cardassian Union was particularly rigid about not letting outsiders get involved in Cardassia's internal politics. (DS9: "Profit and Loss")
In 2364, Captain Jean-Luc Picard was offered the position of commandant of Starfleet Academy by Admiral Gregory Quinn on the basis that Quinn needed Picard "close" in light of a looming conspiracy. When Picard learned this, he explained to Quinn that he was "not good at politics" and felt that there must be others "better suited" for the role. When Picard turned down the promotion, Quinn confessed that he had been "playing politics too long" and that perhaps, because of his, he saw conspiracies everywhere. (TNG: "Coming of Age")
In revealing his desire in the success of Vulcan reunification, Spock explained to Jean-Luc Picard that "the union of the Vulcan and the Romulan people will not be achieved by politics or by diplomacy, but it will be achieved." (TNG: "Unification II")
When Benjamin Sisko and Odo attempted to explain to Federation President Jaresh Inyo about Starfleet's attempt to overthrow the Federation government in 2373, Inyo explained that had served in politics for 70 years, and as such he stated that he was "no stranger to overstatement and exaggeration" but resolved that what Sisko was suggesting was "the single most astonishing accusation I have ever heard." (DS9: "Paradise Lost")
During the waning days of the Dominion War, Chancellor Gowron began to feel threatened by General Martok's feats in battle, leading Gowron to humiliate Martok by sending him on reckless missions. After a series embarrassing defeats, Worf finally came to the conclusion that Gowron feared that Martok may challenge the Chancellor's position. Martok, however, did not share these feelings, explaining that he was a soldier and that he had no interest in politics. (DS9: "When It Rains...")