The point is not to shut the sweatshops down, but to create solutions that will fix the problem rather than create further problems.

So big companies who have the buying and bargaining power need to start demanding that decent minimum wages are set, and that the workers are being paid at or above that wage. They need to ensure that unions are allowed to function, and that basic workers rights are acknowledged. Sweatshops are allowed to prosper because they are the cheap and easy way out. If companies stop taking that easy way out and instead start demanding proper conditions, then it will begin to solve the problems. They also need to stop pressuring governments into creating these free-trade zones for their own benefit with no thought of the human cost.

It's a massive and very complex problem, and for consumers there's not a great deal that can be done to directly help solve it. One of the best actions you can take is to stop supporting the companies who use sweatshop labour (which can be difficult, I know I'm not 100% guilt free by any measure). You can also let others know about it and try to increase the awareness. It's very easy to ignore it all because we don't have to experience the fallout from it.

If you're interested in the subject matter and want to learn more, pick up a copy of Naomi Klein's 'No Logo' book. Recommending it has become a bit of a cliché, but that's mainly because it's a great book that is widely available. It can be a little heavy at times but she's a good writer and covers a lot of good points.