Commercial banks actually create the money (by issuing loans) that is used to buy houses (mortgages) and stocks (leverage).

Central banks affect this process by adjusting the rate to which they lend to the commercial banks, and by quantitative easing /tightening which has a similar effect on long term rates.

Rates are low, more loan value is issued (because the income stream servicing the loan translates into a larger loan amount), asset prices go up. And conversely.

The same way previously created money ends up being used for anything in the private sector: by the actions of individuals, businesses, and non-governmental organizations. If money is cheaper to borrow, they may choose to borrow more, or take on more risk, or what have you.

But money does not "go into assets." That's a misconception. Money trades hands: For every buyer of a house there is a corresponding seller, and for every buyer of a share of stock there is a corresponding seller. Asset prices can rise, or fall, with each trade.

> How does newly created money (which first goes in commercial bank reserves) finally ends being used to buy houses and stocks?

Well, you have some newly created money, whilst the demand for holding money balances (which depends on the price level and the volume of economic activity) stays the same. So what happens is that money is exchanged away like a hot potato until the demand for money balances rises to match the extra created money. In the short run, this is a mixture of higher prices and a higher volume of expected economic activity, both of which would raise asset prices.

The economy is always inflationary. Money today is worth less than it is tomorrow. Money that the bank has is just rotting away, becoming less valuable over time. Banks need to take the cash they have and invest it in something to offset the inflationary losses. Because bonds weren't paying much interest, it was a better return for the bank to loan out the money for mortgages, investors, etc. Eventually those loans become a part of someone's paycheck or into their bank account (ie home sale that ended up with a 2-300% return). Compared to the bank buying bonds which essentially removes money from the economy.