Agreed in that there is no one way in which foreign policy decisions are made, although the Constitution clearly designates the President as being in charge of this area of government. In the present day, the President relies on a group of key Cabinet advisors to help him with foreign policy advice. They meet, usually daily, in a room in the White House called the Situation Room. One type of decision making process within that room might look something like this:
1) The CIA Director presents the latest information on a situation
2) The National Security Advisor assesses the threat to the United States in that situation
3) The Secretary of State gives advice about what the US decision/position should be
4) The Chairman of the Joint Chiefs reviews what our military options are
5) The Secretary of Defense advises what our military posture in this situation should be
6) The President makes a decision on a course of action
Sometimes this process happens several times a day. Sometimes the Vice President will be in the room to offer his perspective and so he will be up to speed on the latest situations in case he has to take over for the President.
In my opinion (as someone who has taught American Government as well as International Relations at the college level) there is no single process of foreign policy decision making that must be followed in a democracy. Even in a democracy, there are a number of ways that foreign policy decisions may be made.
In general, in a democracy, foreign policy must be made in such a way that the peoples' representatives have a chance to make their opinions known on the issue. The policy must, in the long run, be acceptable to the people.
So, for example, when George W. Bush chose to invade Iraq, Congress had a chance to vote on the decision. After that, the 2004 presidential elections and 2006 Congressional elections were contested partly on the basis of attitudes towards the Iraq War. There, the people had their chance to make their opinion known.