Here is New York Times Columnist Nicholas D. Kristof on Sweatshops
Here is an article in the New Republic criticizing the Schumber/Roberts attack on free trade. The first few paragraphs give a good summary of what trade does to boost production. (Note: I would link to Schumer's original article but it is not available free online). But here is another blogger being less kind to Schumer on this issue.
If this is all confusing to you, let me try and explain comparative advantage using the following example. Let us assume there is a doctor and a secretary. The doctor has an absolute advantage in both surgeries and typing (he is the fastest typist in the world). In autarky (i.e. the position of no trade) he does a good number of surgeries but also a lot of time consuming typing. The secretary is unemployment or working at a lower wage job.
Comparative advantage says that it is advantagous for the Doctor to hire the Secretary to do his typing for him. This way he can concentrate on surgeries (boost his output on surgeries, where he makes a lot of money) and leave the typing to the secretary. It does not matter that the Secretary is a slower typist than he is. What matters is that by hiring the Secretary, he leaves more room to specialize in a field he can make a lot of money in and boost overall output. The Secretary is also better off because she is at a nice job with the Doctor whereas before she was either unemployment or working for much less money.
E-mail me if you are still having trouble.