Essentially all the Evil Overlord needs to do is coopt the current technology of Social Meida platforms to monitor the population and exert control. As the product for Facebook, Google and other Internet sites, your browsing habits and other metrics are constantly recorded, updated and sold to various customers. While today it is mostly advertisers, there is no reason that Facebook, Google etc. can't bundle and sell your information to the FBI, CIA, NSA (or the Mossad, MI5 or the FSB, for that matter. I'm sure they would for a high enough price).
Even better for the Evil Overlord, he can use these platforms to indirectly manipulate the population. Facebook has been caught tampering with newsfeeds and "trending", modifying what users see, and Google can modify their algorithms to determine what comes up to the top of a search page. More directly they can also punish users (for example, they have demonetized popular Youtube channels so conservatives make no money despite having thousands of views).
Even more insidious manipulations are possible. Consider Canada's government is pushing something called the "Carrot App". The webpage makes it sound pretty benign, but when you look at it more fully you see:
Creepy Canadian App Gives Citizens Points for Making Government-Approved Choices
People who use the app are given points for "engaging in government-approved messages.", a rather Orwellian concept when you think about it.
Furthermore, even when you are not using the app:
” In order to use the app, users are giving Carrot Insights and the federal government permission to “access and collect information from your mobile device, including but not limited to, geo-location data, accelerometer/gyroscope data, your mobile device’s camera, microphone, contacts, calendar and Bluetooth connectivity in order to operate additional functionalities of the Services.”
It doesn't take a huge amount of foresight to imagine the Canadian Government might soon make installation of the app mandatory for every phone and mobile device sold in the country. How long after that will accessing government programs and services be contingent on your use of the app?
China has also developed something similar, where people get social credit points for adhering to the party line, reading government approved websites and making "approved" comments and votes.
So Big Brother can most defiantly use the Internet to impose a dystopian "1984" like society.
How to fight this would be difficult, the rebels would need to either find ways to transmit information over the internet infrastructure without being detected or revealed (Tor, VPN's, encryption), or more likely revert to things like Samizdat, snailmail and word of mouth to bypass the Internet entirely. This may be preferred especially if devices and programs like Siri or Alexa are routinely installed in buildings to do remote monitoring and spying.
Other hacks the rebels could try include discovering ways to flood the data collection functions of Facebook and Google with nonsense results, or directly attacking and disabling the server farms which house and control these companies infrastructures.
You thought this was just fiction, didn't you?