How do governments/central banks "inject" money into the markets?

In recent weeks I keep reading about how this or that central bank is “injecting” or “pumping” X billion euros or dollars or whatever currency into the markets to keep them liquid. How do they do this? Is there a physical transfer of reserve cash?

As I understand it, they allow the normal banks to lend more money from the Central Banks.

So a X billion Euro injection, would mean that the banks could loan X billion Euros more from the European Central Bank.

The reason for this, is that the normal banks now hesitate to loan each other money (as they might think the reciever might go bankrupt) and some banks can therefore not cover their (usually) short-time debts.

This injection allows them to lend money and cover them.

The money being lent, is either from the Central Bank reserve, new money being printed, or money the Central Bank loans from other places.