Matt Yglesisas sums it up properly—you defeat them by denying them ports to sell their goods and the reason piracy is so out of control is because, as I noted at the time it was happening, they decided to get rid of the Islamic Courts Union (ICU), the only movement that stood a chance of reunifying Somalia, stopping warlords from raping and murdering whoever they wanted, and, incidentally, stopping piracy.
So, if the Obama administration is serious, what they need to do is a 180 degree turn and support the successors to the ICU. Yes, that will mean supporting some Islamists, but so what? If the US can do business with and support Saudi Arabia, which is even more socially regressive than the ICU ever was, and funds foreign terrorists who attack the US, which the ICU never did, it can make a deal with Somali Islamists, who in any case, are mostly interested in having some basic law and order in the country so that warlords don’t rape their teenage daughters and murder whoever they feel like.
Given a choice between having my teenage daughter raped, and a little bit of Islamic law, I know which one I’d choose. Perhaps America should let Somalis make the same choice. As a side benefit, there’ll be a lot less piracy, because the new government will want normal trade and diplomatic relations (and aid) and the price for all that can be to crack down on the pirates, which as Matt notes, can only really be done on land.