It's a bit more interesting than 'the central bank sets interest rates'.
Simplified: the central bank decide on an interest rate that they want to see. By itself that decision doesn't do anything.
What happens next is that they buy and sell government bonds in the open market. The interest rate can be seen as the inverse of the price of bonds.
If the central bank wants to see a lower interest rate, they buy bonds with freshly printed money to drive up their prices, ie drive down the interest rate.
If the central banks wants to increase the prevailing interest rate, they sell government bonds from their inventory and essentially destroy they money they receive in return.
So even when the language of modern central banking talks about interest rates, they still change the quantity of money to implement that.
(This is all simplified, especially with the interest on excess reserves that was popular with the Fed for a while. And there's also repos and reverse repos etc.)
This describes how central banks operated in the U.S. before 2008 and in Canada before the 1990s. The Federal Reserve and the Bank of Canada both set a target for the overnight interest rate, and then they hit that target by doing open market purchases (or sales) of bonds, effectively adding funds to (or draining funds away from) the overnight lending market. By changing the quantity of funds, they influenced the interest rate.
What changed is that both central banks introduced interest payments on balances that banks hold at the central bank. Previously, these balances earned 0%. With this new tool, they could directly set the overnight interest rate by adjusting the rate paid on these reserves, eliminating the need for regular open market operations.
https://www.newyorkfed.org/markets/domestic-market-operation...