How exactly does a central bank determine how much to cut/increase interest rates? We all know under what circumstances a central bank tries to cut interest rate and when it tries to increase interest rates, but how do those people know exactly by how much it should change?

I mean, there can be some trial and error, but what are the targets they chase and how exactly do they calculate the money demand, etc. There should be some basis to their conduct.
They don't know for certain. It's an inexact science. They do the best they can.

Alan Greenspan was known for pouring over all the economic data available for hours while mostly in the bathtub trying to make sense of what was happening in the economy. But ultimately, it came down to making an informed decision based on knowledge, reasoning, experience and intuition.

Policy objectives (which are quasi-political) can also come into play as sometimes desired results can compete. The classic example of this is economic growth vs. inflation.

Critics of government monopolized central banks argue that it is impossible for any single individual or group of policy makers to choose rates correctly and overnight interbank lending rates should be allowed to float freely and be determined by the market vis-a-vis supply-demand equilibrium. Hence the popularity of LIBOR and to a lessor extent EURIBOR as these are closer to market pricing than, say, the Fed Funds Rate. However, these are still only averages of central bank policy decision and, therefore, are not purely market-driven.