Although government borrowing does increase the money supply, that is not usually the reason why the government borrows. The federal reserve has the responsibility of regulating the economy by changing the money supply. They have a number of ways that they can use to expand or contract the money supply.
The primary method they use is to encouraging banks to lend more or less. The most common method they use is changing the FED interest rate which they started increasing last Spring. This is the rate banks pay to borrow from other banks. The FED can also change the discount rate which is the rate banks pay to borrow from the FED. Also they can change the ratio of deposit to loans and investments. By changing these rates, banks are encouraged to tighten or loosen their loan policy which increases or decreases the money supply.
The FED can buy or sell treasury bills. When they buy treasury bills from the treasury, funds from a Federal reserve account is transferred to a treasury depository account, again increasing the money supply. However most often the FED will buy treasury bills on the open market. This will increases the volume of bank reserves held by depository institutions.
There are are a number of other tools the FED can use such as changing the margin rate on purchases of securities, closing banks, and changing various rules banks operate under.
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