If hard power is characterised by the use of military force to project our will, then the essence of soft power lies in values, in our culture and in the way we handle ourselves internationally. Soft power is about creating a sense of legitimacy for a nation's international aims.
To understand what's happening in US foreign policy you have to start with 9/11. Before that date the Bush administration had been running on a fairly traditional realist platform; no more nation-building, and a broadly unilateralist approach to foreign policy. After 9/11 the Bush administration realised this had to change.
Credit must be given to the Bush government for the speed in which they realised traditional conceptions of threats to national security had changed. However, what they are still struggling with is how to combat diffuse non-state actors, primarily in the form of al-Qa'ida.
Hard power, which is so successful at one level, does play a role in the war on terrorism, but it is not quite the role you first expect. Hard military power did topple the Taliban, something soft-power was in no position to do. However, if you look at the number of Taliban fighters actually killed in Afghanistan, you're looking at maybe no more than a third.
In order to win the war on terror therefore, you also need soft power. You need the stick but you also need the carrot. Bombing and land invasions of countries harbouring and fomenting terrorism are important, but we must employ greater public diplomacy in order to attract people away from militant Islam. If the US would divert even 1 per cent of its defence budget to public diplomacy it would signal a quadrupling of the budget currently given to those looking to implement soft power rather than hard.
To conclude, what is important is not soft power or hard power alone. It's a combination. Our military power stopped Soviet aggression, but it was our soft power which fostered cultural progression and sympathy to our aims and stopped states from falling into the hands of communism.