A lot of information on the Cyber War against the United States is kept secret, since if the attackers know which of their operations are being observed, or even known about, they will take steps get their work back into the shadows. Half the battle in Cyber War is knowing you are being attacked. The best attacks, especially to steal information, or set up monitoring programs, work best, if at all, if they are undetected.
What is known is that the U.S. Air Force has taken the lead in developing Cyber War weapons. Air force hackers are usually the first to spot new enemy intrusion techniques, and are believed to have created powerful intrusion tools and techniques themselves. It's telling that intrusions of Department of Defense computers get publicized, while you hear little about such attacks made on other countries. It could be that the United States is not making as many intrusion attempts as are known Cyber War users like Russia and China, or that most of these intrusion attempts go undetected (whether they succeed or not.)
Another reason for the large number of detectable attempts on Department of Defense computers is that the United States is the highest profile target for such attacks. The detectable attacks are often by amateurs, although some of these have been tracked back to government computer systems in Russia and China.
The U.S. Air Force has many electronic warfare aircraft, and access to U.S. electronic warfare satellites. The plan is to use all these resources in any future Cyber War, finding enemy vulnerabilities wherever and whenever, and exploit them as quickly as possible. With so much of the world's electronic communications going wireless (including via satellites), this gives the air force lots of opportunities. But until there's an war, the public won't know how extensive the American Cyber War arsenal is, and how effective it can be.
The U.S. Department of Defense believes that some twenty countries have established Cyber War organizations, and are trying to develop tools and techniques for attacking American military and civilian targets, via the Internet, in the future. In some respects, these Cyber Wars have already begun. In the last year, the number of intrusion attempts on Department of Defense computers has tripled (to over 500 a day.) The actual increase may be less than that, because as the Department of Defense increases its Internet defenses, it becomes better able to detect intrusion attacks. The number of intrusions that succeed, or at least the ones that were discovered, has been going down.