Adams used satire in The Hitchhiker's Guide to the Galaxy to show the absurdity of modern life, and how things that we consider of great importance are actually insignificant in the larger scheme of things. For example, Arthur is worried about his house being destroyed for the construction of a highway bypass; this problem becomes unimportant when the entire Earth is destroyed for much the same reason. Many of the situations mirror situations, events, or institutions on Earth, but are exaggerated for comedic effect. Galactic bureaucracy is shown to be staggeringly inefficient and bloated, with the Vogons being an entire race of inefficient and bloated creatures whose sole purpose is to help block progress and create paperwork. The destruction of an entire planet (Earth) is seen by alien races as unimportant; on a galactic scale, planets and races are destroyed every day, and so Arthur's concern is mocked and ignored. By using easily-identifiable scenarios, Adams was able to show the absurdity in everyday life, and how constant worry over small issues is counter-productive.
The first satirical example is when the Vogans destroy the Earth to build a hyperspace bypass. They need the bypass to travel faster but almost immediately the improbability drive is created and cancels the need for the bypass. The galactic bureaucracy reflects human bureaucracy and the absurdity of the galactic one sheds light on the human one. Recall that the Vogans said the plans to destroy Earth was located in our regional representation office at Alpha Centauri and its our own fault that we never bothered to show up and dissent.
I'm actually writing on essay on this right now... multiple examples of satire are worthy of our attention but three googd ones are the vogans who are used to satirize government employees or perhaps even lawyers (considering all their paperwork), Zaphod Beeblebrox is a representation of the stupidity of politicians, and the recorded message at Magrathea (Your death may be monitored for training purposes) pokes fun at the ever growing use of automated systems over the phone. I hope this helps you! :)