I will spend some time on this topic, because the decking system blows goats. Since I'm a computer guy myself, I can't stand the way that Shadowrun handles decking. Too much of what they call impossible, or difficult, is possible today and not that difficult.
Public access to the matrix is probably where technology excels the most. The Internet that we all know and love has evolved by several generations into what is known in 2054 as the Matrix. Trids are almost always hooked into it and a user can jump around the different information services that are publically available. The amount of information that a user can come across is truly staggering, though not always useful.
These are basically phone booths that have a turtle interface to the matrix. A decker who knows what he's doing can override the kiosk with his deck and go full tilt into the matrix. The kiosk has a headset (like a phonebooth's handset) as well as a jack for the jack-capable.
"What does my character know how to do?"
Most characters should know the basics about how to operate a trid system. This little bit of knowledge can lend itself greatly to searching for information using a trid connection, as well as a public kiosk.
Think of a number. Multiply that by the number of letters in the most inane subject you can think of. That is roughly the number of channels available in the larger markets (LA, Seattle, Denver, etc...). The OJ Channel!
As an example, CNN has dominated the field and evolved to meet the needs and wants of the current times by branching their news operations into over 50 markets.
For a few extra Nuyen a month, you can get a full speed matrix connection (fiber is everywhere) for your trid or computer connection. If you connect your computer, then it is set up similar to a corp's computer system; an outside decker, or program, could get into your computer unless you spend alot of time making sure you don't have any security holes.
For those homes that do have a matrix feed, their trid system is the main piece of entertainment and information technology in the house. Everything is piped through it including music, news, entertainment, communications, and matrix access.
Corporate Computer Systems
The large heterogenous computer systems that the corporations use are indeed processing beasts. The security is tighter than any computer in existence today and the increase in raw power is beyond current theory. This is due to the massive use of photonics, as well as some bio/optic/electric systems. The different nodes are different types of computers (Hey, they're nothing but tools, right?) and they all have a specific job to do. Breaking into them is not a simple job. That is why deckers are so rare to find and so skillful.
A system that has a sculpted environment will, more often than not, be able to impose that reality onto an incoming decker. When this happens, the GM and decker(s) should go immediately into role-playing mode. Encounters in sculpted systems should be resolved in this manner due to the fact that a sculpted system can have it's occupants look like anything. The lowliest security decker could have an icon appear as the nastiest piece of ware and the blackest ICE could be tse-tse flies. This type of matrix play would make deckers a more inviting character type to play.
Media storage should have progressed enough so that a decker going in to the matrix should be able to carry every program he has with him (granted, not all in memory) and still have enough storage space left over to return with a few hundred copies of the Smithsonian archives. IBM of today (Itty Bitty Machines) is the leader in magnetic storage development. They are doubling the amount of data that can be stored on a platter every year, and they don't see an end in sight. I'll go along with memory (RAM) being expensive, but storage (online or offline) should be super cheap for even the largest amounts.
These suckers are very fast. The step from flat screen to VR would never have succeeded if the response hadn't seen an incredible increase in speed (he says through the drool thinking about a truckload of SGI's).
I'm of the belief that the Unix operating system is the basis of the matrix, as it is of the Internet of today. If you disagree, well, you're sadly mistaken. With this in mind a good number of utilities, native to each system, should be available for use by a decker. One that comes immediately to mind is "grep". This is a powerful search utility that most any system would have.
Again, being a Unix guy, security is an extremely important issue. Deckers have the ability and prowess to circumvent many countermeasures, but keep in mind that a normal guy isn't going to have clue one on how to deal with even the most insecure system.