It is difficult to measure the money supply, but most economists use the Federal Reserve's aggregates known as M1 and M2. Gross domestic product, or GDP, is another government statistic that is tricky to measure perfectly, but nominal GDP tends to rise with the money supply. Real GDP, adjusted for inflation, does not track as cleanly and depends much more on the productivity of economic agents and businesses.
How the Money Supply Affects GDP
According to standard macroeconomic theory, an increase in the supply of money should lower the interest rates in the economy, leading to more consumption and lending/borrowing. In the short run, this should, but does not always, correlate to an increase in total output and spending and, presumably, GDP.
The long-run effects of an increase in the money supply are much more difficult to predict. There is a strong historical tendency for asset prices, such as housing, stocks, etc., to artificially rise after too much liquidity enters the economy. This misallocation of capital leads to waste and speculative investments, often resulting in burst bubbles and recession. On the other hand, it is possible money is not misallocated, and the only long-term effect is higher prices than consumers normally would have faced.
How GDP Affects the Money Supply
GDP is an imperfect representation of economic productivity and health, but generally speaking, higher GDP is more desired than lower. Rising economic productivity increases the value of money in circulation since each unit of currency can subsequently be traded for more valuable goods and services.
Thus, economic growth has a natural deflationary effect, even if the supply of money does not actually shrink. This phenomenon can still be seen in the technology sector, where innovations and productive advancements are growing faster than inflation; consumers enjoy falling prices of TVs, cellphones and computers as a result. (For related reading, see: The Top 6 Ways Governments Fight Deflation.)