Truth be told it varies quite a bit depending where you are and what you are doing.
For telecom field systems we are using the IRIS communications system and it is the first really digital military comms system out there. It is actually so good that the Brits have even bought into it, and the US Marines are looking at it last I heard. Information on it can be found at this link
http://www.gdcanada.com/iris/
Now in garrison we are about in line to slightly behind WRT many large enterprises when it comes to computers, telephones, and other tech and the way we use them. We do not have a lot of the newest and greatest to go around but most of it is quite useable and and sufficient for the mission. For example on our normal network nationally we should be converted to Windows 2000 by now, but we have pushed it to 300MHz workstations, which can be slow at times but still useable depending on what people are doing.
As for outside training, the military usually tries to teach everything in-house even for the ever quick pace of IT. There are occassional courses that have been run by educational institutions and the military has sent them on it, but for the most part if you want to keep up do it yourself. If you are Reg or Res the military offers money for educational upgrading but mostly on your own time, especially when you are just starting out in your career. When you are getting close to your 20yrs the military has a program that you can use called SCAN that allows you to go to school full-time while they still pay you.