First, we must note that there are plenty of people who would argue that NAFTA (the North American Free Trade Agreement) does not show that free trade is a good thing. There are those who argue that free trade has helped to weaken the US economy and has allowed jobs to leave the country more easily than they previously could.
On the other hand, many people, particularly mainstream economists, believe that NAFTA has proved that free trade is a good thing. They tend to argue that NAFTA has increased trade between the US, Mexico, and Canada. They say that this is a good thing because it allows more jobs to be created in the US. These are jobs in industries that export goods.
We can see in this link, for instance, that there were 2.6 million jobs in the US that were “supported by” exports to Mexico and Canada in 1998. More recently, this link argues that the US economy had 20 million more jobs in 2010 than it did when NAFTA was signed. It also notes that trade between the three countries has tripled. This should mean more export jobs in the US as well as cheaper goods being imported from Mexico.
In these ways, we can at least argue that NAFTA proves that free trade is a good thing.