First of all, there's a lot less paper on board, and a lot more computers. You don't see log books or many paper documents on the ship. Standing watch, you have a PDA or PC to record information on, and this data goes into the boats network. This allows for much more effective use of all that information. The system automatically does analysis, and alerts the crew to any problems, or potential problems. As a result of all this automation, some watches have been changed, usually to reduce the number of people needed, or eliminate the watch entirely. For example, those who actually "drive" the boat (one of the more critical watch duties) now consist of only two people. There's a pilot, and a co-pilot. These are senior petty officers, who have computers to monitor all the instruments that previously required four or five people to deal with. The two pilots also interact with the sub differently, using large touch screen (19 inch flat screen displays now so common in the PC world) to made adjustments to ship systems. There are some backup switches (of the traditional kind). But the pilots rarely have to use them (and then usually for drills, to make sure they still know how to do it old school.)
One of the most dramatic changes has been in the periscope. The old fashioned one is gone, replaced by electronic cameras, that can take 360 degrees worth of pictures (day or night) and then pulled below again. Much less risk of being spotted. And the pictures are HDTV quality. You also get full color video,. There's a traditional looking periscope, but it does not penetrate the hull, as well as one that is attached via a cable. In addition, there is a new electronic "periscopes" that views the surface from underwater, and uses electronic analysis to create a clear picture of what's up there. All of this is viewed on a large flat screen display. No more squinting into a periscope eye piece. All of this is not just for providing better visuals, but for getting better information to the crew faster, which provides a time advantage in combat. That's a lifesaving advantage.
A lot of things sub crews have been complaining about, for decades, have been fixed in the Virginia. The escape chamber is now entered from the side, not the bottom. This is much appreciated by the SEAL teams that often ship out with U.S. subs, because they often leave the boat while underwater, via the escape chamber. There's also a second loading hatch, just for weapons, which cuts the time and hassle of loading stuff into the boat. Perhaps most appreciated is the fact that everyone has their own bunk. For years, the most junior crewmen had to share a bunk, because there wasn't enough space for everyone to have their own. Another much appreciated fix is to the toilets, making them much less likely to back up on you the pressure settings were not just so.
The ships computer network not only plugs into just about every piece of equipment on board. There are jacks all over the place, so you can plug in your laptop, or any other device with a network connection. The boat has email access (for when the sub is close enough to the surface to connect with the military communications satellite network overhead) to send and receive messages. This is great for morale, because in the past, the crew was cut off from the outside world for months at a time, as they cruised underwater. In the past, there was a special underwater communications system. But it was very slow, and just used for military communications.
The first Virginia class sub has entered service with the U.S. Navy, and it's a very different type of sub. Many of the changes are subtle, but they all contribute to make the submariners life quite different from past experiences underwater.