The Matrix in Dark Metal canon is an immersive evolution of the internet. It can still be accessed to a limited degree by something akin to web browsers, but the majority of users are expected to be connecting via datajacks - cyberware implanted and connected to the nervous system, such that a user has a direct feed.
Of course, as with all things, how much you're willing to spend makes a difference in your experience. Users without the ability or funds (or desire) to have a datajack installed may use virtual reality gear - anything from bulky headsets and gloves (even outdated keyboards) to much lighter 'trode nets that read electrical impulses from the skin. (Many supernaturals are limited to VR gear or 'trode nets because their physiologies aren't properly compatible or they can't or won't have cyberware installed.) Reaction times are significantly slower, sensory immersion quite limited, and some areas may be completely inaccessible.
Even with datajacks, the experience varies enormously. Depending on the speed of the 'jack and the sophistication of the cyberdeck or other connection being used, the resolution may vary from jerky and grainy up to a quality nearly indistinguishable from reality (although rumors of areas of Matrix that really can be mistaken for reality remain - so far - just rumors). The quality provided by a given section of the Matrix depends in part on the maintainers of that section, and in part on the gear of the user, since many cyberdecks and add-on icon packs can include their own default graphics settings at the whim of their owners.
Access to the Matrix is common to the point of ubiquitous in Bright areas. Most Bright citizens will either have a home feed or visit cybercafes (and similar establishments). Private feeds become less common in Grey and Dark areas (although theft of service is rampant), but cybercafes do a brisk business. Quality of gear varies with the price required; many Dark cafes don't offer jack connections, or if they do, they're slow and low-quality.