Before I explain that, let me explain what's changed fundamentally about the Matrix rules. Throw EVERYTHING you knew from any other edition out the window except the fluff. It'll be easier that way.
Every electronic device has two ratings, which are part of their hardware. Data Processing and Firewall. Data Processing is basically like the clock speed of your processor and RAM on modern computers. It's how fast the device can take data in and spit it back out again. Firewall is security - your firewall, anti-virus, and general security all rolled into one. Now, deckers have two additional attributes for their cyberdecks - Attack and Sleaze. Attack is just that - electronically smashing any icon you come across, potentially causing physical damage to the hardware via short circuits, overheating, etc. Sleaze is how you hide your actions on the Matrix. If you remember ANY other edition's attempts at hacking, you'll know how fragging SIMPLE that is and how much it just makes logical sense.
Now, here's the kicker. Because of the new Matrix security protocols implemented by Grid Overwatch Division (aka GOD) from the Corporate Court, the second you perform ANY illegal activity on the Matrix, the clock starts ticking. What's illegal? Anything that involves the Attack or Sleaze attributes of your deck in any way, shape, or form. You start generating what's known as the Overwatch Score (OS). Every single hit that any device gets defending against your actions adds to your OS. If you reboot your system, your OS is also reset but you'll have to start over with whatever you were doing. If you don't reboot in time and your OS score hits 40, then that's when a Convergence happens. Three VERY nasty things happen. First, your deck takes enough damage to potentially brick it. Second, you're ejected from the Matrix and immediately take Dumpshock damage (if you weren't kicked out when your deck melted, that is). Third, your PHYSICAL LOCATION is transmitted to both the host you were accessing and the host you were hacking. So a very likely scenario is that you will wake up to find your 200,000¥ cyberdeck is nothing but a puddle of silicon and plastic, you've got a splitting headache and a nosebleed, and you've got two different heavily armed security teams discussing amongst themselves who gets to bring you in for "aggressive questioning" or just shoot you in the face and leave it be. Oh, and the first illegal action you perform, you get 2d6 OS every fifteen minutes after it happens even if you don't do a single thing after that.
Now that we've got that out of the way, we can talk about the skills. There's six skills pretty much every hacker is going to take: Computer, Hacking, Cybercombat, Electronic Warfare, Hardware, and Software. Computer covers basic non-illegal computer use - the search that you mentioned before. Hacking involves illegal Matrix actions like trying to gain access to another system. Cybercombat is how you deal damage to other icons in the Matrix (which does a LOT more heavy lifting than it did in any previous edition of the game). Hardware and Software are more or less similar to the old B/R skills if you've played a previous edition. Finally, Electronic Warfare is...well, it involves signal manipulation and spoofing and...it's really hard to explain in a single sentence but once you read the Matrix chapter of the book, it makes PERFECT sense I promise.
