What are the steps that would have to be taken to impeach him for his acts? And on what grounds would such an impeachment be made?
To impeach a US President, a majority of the House of Representatives must vote to impeach him. At that point, he is sent to trial in the Senate. The trial is presided over by the Chief Justice of the US Supreme Court. If 2/3 of the Senators vote to convict, the President is removed from office, and the Vice President becomes President.
As for grounds, technically, there don't have to be any. Chief Justice Rehnquist wrote a book about impeachment and noted that ultimately, it was a political matter. This was, incidentally, before he served as presiding judge at the trial of Bill Clinton. However, traditionally and in practice, the President would have to be charged with a crime.
In this case, the crime would take one of two possible forms. The Constitution of the United States says that only Congress can declare war. He could be charged with unconstitutionally declaring war against Libya by taking an aggressive military act against government forces.
The whole concept of "declaring war" arose out of 18th century European customs, and is a bit dated, and presidents Truman, Kennedy, and Johnson managed to get us into what were rather obviously wars without actually declaring war, and so some Congressmen decided in the '70s a little bit more definition was needed and they passed the War Powers Act. It defines what the President can and can't do militarily and when he needs to seek Congressional authorization to do it. It would prbably be that act that Representative Kucinich would claim had been violated and therefore would create an impeachable offense.
Unfortunately, the one time anyone in Congress tried to enforce the War Powers Act, during the Iran-Iraq war when our naval forces were aiding Iraqis in defense against Iranian attack, the attempt was rejected. I never read the opinion, because that was pre internet, but it was dismissed as a polical issue by the Appeals Court.
At any rate, Obama isn't going to be impeached, at least not during this term and not for this. As Rhenquist noted, it really is a "polical mater", and the political will doesn't exist for either impeachment or conviction.
ETA: Since we now live in an internet era, I finally looked up the case. It's Lowry v. Reagan.
http://dc.findacase.com/research/wf...ac./FDCT/DDC/1987/19871218_0000272.DDC.htm/qx
It's not as stupid as I had thought. (Really, court decisions rarely are). The essence of the opinion is that if Congress thought that this was a situation where the War Powers Act applied, they could have said so by voting a declaration that the conditions existed. Instead, there was considerable debate, and no vote was taken.