The media influences political discussion in many, many ways. A few of them are:
I) It defines what is object of political discussion. When a journalistic report is made on a subject that wasn't a matter of public concern, it has many more chances to become a public concern.
II) One implication of the previous item is that the media has the power to shape what is believed to be a public matter.
III) It can also define what is not an object of political discussion. If the media doesn't report on a public demonstration, for example, it is saying that it is not important and it doesn't deserve attention.
IV) The media has the power to direct the public's attention. That means it is able to define what the public's attention will turn to. If it is to one or another scandal, corruption case, etc.
V) The media can change the course of a political discussion. Because it is able to direct the public's attention the media can directly influence the course of a public discussion. It can define if at a certain point the public will be paying attention to Congress or some politician's personal life, for example.