Traditionally the Fed has bought and sold Treasury bonds on open market transactions.
Beginning with the 2008 GFC, this was expanded to buying "distressed assets" (https://blogs.wsj.com/economics/2008/11/10/fed-takes-step-in...). This was, and remains, controversial (as noted in the WSJ link), and poorly understood (I'm still not certain I grasp it well, let alone fully, myself).
My understanding is that the Fed's goal isn't profit, but of buying money into, or selling assets, and hence money out of existence. The Fed's asset-buying targets are better thought of as liquidity-injection targets (where liquidity is money created by the Fed to be injected into the economy). The Fed stabilises asset prices as a buyer of last resort, incidentally to its primary goal of both ensuring sufficient money in the economy and in creating greater ceertainty in asset values which allows banks to function.
The Fed can always buy assets or lend money, as it has the sole power (save the US Treasury) to create money without restriction. And in practice, it makes profit on these transactions (which is contributed to the US Treasury).
The distortionary effects on risk and incentives ... remains fuzzy to me.
This is largely my own conceptualisation, it seems generally to agree with other explanations, and smells strongly of MMT.
I may be badly mistaken, however.