Satire serves to point out the folly and ridiculousness of either a person, event or thing. To get started on your satire, you first have to have a topic to write about. Usually, satirists write on a subject that is current, as a topic straight from the headlines catches the most reader's attention. There are several go-to topics to satirize that have been used for centuries
Satire on politics is as old as caveman drawings. Politics is one of the first subjects to have ever been written in satire. See how other satirists have approached political issues -- as there are many ways to do so -- and compare various styles. Examine some political cartoons as well. Some political satirists are especially biting while others are more tongue-in-cheek and thoughtful. See Resources for a variety of examples of political satire.
Movies / Television
Write about films getting released in theaters or TV shows just premiering. Not only do movies and television sometimes satirize various subjects, the films and television programs themselves may also be satirized. For example, the "Scary Movie" franchise points out the ridiculousness of horror movie tropes. Also, "Murder by Death" (1976) poked fun at self-serious detective films and film noir. Sometimes movie critics will satirize poorly regarded films, so it may be well-advised to read film reviews from popular and reputable papers or magazines.
As the common saying goes, truth is often stranger than fiction. Whether from the national or local headlines, events happen just about every day that will make one question human logic, such as a bizarre local crime (i.e. a lawyer moonlighting as a hooker. See True Crime Report in Resources for this story) or a local event such as the Renaissance Fair, the State Fair, a mayoral election campaign, or any other type of public incident. You can also go more broad with a national incident, such as the Lindsay Lohan trial or Paris Hilton getting released from jail. These are prime examples of good subjects to satirize. (Note, also, that the examples listed here will become outdated with time. Make sure your current events are in fact current when you write them, enough that people are still "buzzing" about it)
The well-publicized antics of celebrities and famous people have been the subject of satire for a very long time. According to the Bandersnatch website, if you choose to satirize a public figure, the figure should preferably be high-status and well-known, since they have a harder time suing. Also, make sure to make it clear that the piece you write on any particular person is indeed a satire and thus fake. You can also satirize the latest fads in pop culture, such as the emergence of complicated gadgets or popular fashion statements.