What's the relationship between the Fed and Treasury?

The US Treasury issues debt on behalf of the Government and acts as the Bank for the US Government. It pays the bills for the US Government, stockpiles the wealth, etc...

The Federal Reserve creates the money in circulation. It runs the entire banking system in the country.

A good example of how the two work, is that lets assume today is Day 1 of the United States and we currently have $0.00 as a nation. The US Government wants to build a highway system that costs $1/billion dollars. How can this happen?

First the Congress would approve the bill and the president would sign it. Then the US Treasury would issue $1/billion in Debt. The Federal Reserve would create $1/billion dollars from thin air and buy the debt from the Treasury. Now the Treasury has $1/billion in cold cash. The Fed now holds the debt. Then the treasury begins writing checks to whomever is running the new highway construction operations. This putting $1/billion dollars into the hands of We the people. Who then turn around and go buy widgets from Walmart. The government then taxes us to repay the debt that was issued.