Ideally you would also repeal legal tender laws and allow the free use of alternative means of exchange, which would revert to some form of privately-minted currency that maintains a highly stable value in a market system - probably not the cliched gold standard but maybe some form of currency with a frozen money supply or at least one that increases at a pre-set, known rate, possibly but not necessarily in conjunction with a commodity standard.
Once that happens, it would become impossible to continue the present system of massive regressive wealth transfers by means of minting dollars and giving them to bankers while sapping the middle class's (more like "the 99.99%'s") purchasing power by means of the resulting inflation, and causing the boom-recession cycle because of the large-scale, poorly considered overinvestment caused by taking large amounts of wealth from the middle class (who would spend it on actual consumer preferences) and giving it to leeches (who spend it on speculation).
Actually, you don't even need to end the Fed to do that, you could just repeal legal tender laws. Ending the Fed would certainly help though, and if legal tender laws can't be repealed the next best thing would be to end the Fed and move to some sort of (real) commodity standard, because then at least you wouldn't be able to have the present system of trapezocracy.
^^^This is the closest I've seen to a sane libertarian argument towards ending the Fed. You end the fed and you go to a private money system it is the only possible option. Google "Suffolk system" and you'll get the idea.
I come across way to many libertarians like Chairman Sanchez up there that think that you can end the fed and move to a Bretton Woods style central bank Gold Standard model(which is what most libertarians think of when they say "Gold Standard".
Well you need a central bank(therefore you need the Fed) if you're going to try to enact a national gold backed and pegged currency system. The idea wont work for 100s of reasons.
Now if you were looking at a private money system then it would be a different story, that quite possibly could work. In theory the first step is as wormguy pointed out; you need to end legal tender laws.
But keep in mind all of this is perfectly fine in economic theory. Even if you could prove definitively to everybody involved that the system would be better their are enormous challenges to doing something like this.
