To increase money supply the Federal Reserve keeps interest rates low, this makes it less expensive for people to borrow money and as more loans are taken the supply of money increases. Another way of increasing money supply by the Fed is buying back bonds from banks, in return the Fed gives money to the banks that can be given to borrowers.
If the Fed restricts money supply, this increases the cost of loans. People are now less inclined to borrow money and invest it in the capital markets. As a result, the price of equities in the stock market would come down.
In addition, a reduction in the quantum of bonds bought back by the Fed decreases their demand, and subsequently there is a fall in bond prices.