The core of the Metternich system was that everyone could be an informant. He didn't just have proper spies everywhere and official positions controlling for him, you could for example also as a student report your professor for promoting liberal or nationalistic ideas if you didn't like them or him. So really, there was no telling who could snitch on your every step.

University and Burschenschaften matters specifically were regulated by the Zentralkommission zur Untersuchung hochverräterischer Umtriebe (central committee for the investigation of treacherous activities) founded in 1819 and seated in Mainz, who acted as central coordinator for the pursuits of liberal and nationalistic elements in universities and Burschenschaften and also authors such as Karl Marx or E.T.A. Hoffmann.

Controlling the press is pretty easy. According to §1 of the Preßgesetz established in the Carlsbad Decrees no daily publication or serial exceeding 20 sheets could go to print without approval by a local board of censors. All publications also had to display the names of both publisher and editor under penalty of jail and removal of the publication (§9), so anonymous stuff could easily be pulled from distribution and investigated. When a publication was taken out of circulation completely the editor's name was distributed all around the German Confederation to ensure he couldn't work in that field for at least 5 years (§8).

This whole system directly led to the very peculiar German period of Biedermeier.
Because public life was controlled by the state and filled with spies the middle class relocated much of their social life into their own homes. That time saw the development of proper "living rooms" and, especially in Vienna and the rest of Austria, the still prevalent coffee house culture. Social gatherings were done in small private circles to prevent spying so people could freely exchange poems and such that wouldn't have passed the censors, wealthy middle and upper class sometimes even had private theatres in their homes where they could host indecent plays for their friends.

In Vienna the conservativism gave rise to the Alt-Wiener Volksstück (old-Viennese folk play), whose main representatives Ferdinand Raimund and Johann Nepomuk Nestroy still count amongst the greatest Austrian playwrights. Especially Nestroy had great fun with the censors, continually seeing what he could sneak past them when he had to hand in scripts and always doing the most daring improvs when he played his roles.

Theatre censoring in the Austrian Empire was done by the Polizeihofstelle, more or less regular policemen called "theatre commissars", who evaluated scripts, went to rehearsals and premiers and had full authority to change every aspect they didn't like. But they were just policemen nevertheless, so if you were clever enough you could sneak a lot through since only really racy stuff was sent for further evaluation to the state chancellery. A play passing in Vienna normally meant a pass for the whole Empire while on the other hand plays from somewhere else had to be re-checked since the provincial censoring boards were a lot more liberal, which meant sometimes you could make a short travel to Graz, Brünn or Budapest and catch a play forbidden in Vienna.

I could probably write a whole post about Nestroy, so great was his provocative genius. In 1835 he had to spend five days in jail after he improvised the line "At the table they're playing Whist [a card game similar to bridge]. It's strange that the most intelligent English game has the same name as the stupidest man in Vienna [his sort-of nemesis, the critic Franz Wiest]."
A decade later he went on the stage wearing Kaiser rolls instead of buttons in satire of the emerging scandal that they weighed only half as much as 20 years ago but cost the same. For that he had to spend a night in jail and apologise for it at his next play. When he did the apology he also thanked his jailors for supplying him with rolls by inserting them through his cell's keyhole. I love Nestroy.

Not sure what else you want so I'm gonna leave it here and wait for possible follow-up questions.