The Fed does set the federal-funds rate--the overnight interest banks charge to lend to each other--and surely affects the timing of rate changes, but not the longer-run level.
This is the second sentence of an op/ed in this morning's Wall Street Journal by William Poole, currently a senior fellow at the Cato Institute and formerly president and CEO of the Federal Reserve Bank of St. Louis. The article is titled "Don't Blame the Fed for Low Rates."
Poole is an excellent monetary economist, but this is just wrong. Indeed, his own sentence shows that it's wrong. If, as he correctly notes, the federal-funds rate is the interest rate that banks charge in their loans to each other, how could the Fed possibly set it? Moreover, not only does the Fed not set that rate, but also the Fed is not even a participant--as lender or borrower--in the federal-funds market. The most the Fed can do is influence the federal-funds rate indirectly, mainly by using open market operations. But it does not set the rate.