My understanding is that it will erase the entry from any US DNS server, and demand that any other DNS server abroad do the same, though how successful that would be is unknown. It would also blitz anything ending in .com, .net, or .org
However, it would still block most Americans from those sites even if all it took was using a different DNS server. Think, how many people know how to change their DNS settings? Before you answer, note that I have repaired a few computers and installed Firefox on them, which prompted the owner to ask, “Where did the Internet go?”. One of them refused to believe that Firefox connected to the same internet even after I demonstrated. While you and I have no problems with that, people like my boss, my parents, and the average person on the street will be screwed. And while it is true that there are already ways—(like browser extensions) to circumvent DNS blocking, rest assured that it will turn into an arms race anyways. There is also talk of abandoning DNS anyways, but that is a rather long, technical digression.
Also, this thing isn’t just about the US. Look at the other things that will get you in trouble with US law even if you are abroad and your actions are perfectly legal there, and look at how we are trying to impose our laws on foreign jurisdictions. We threatened Spain into adopting something SOPA-like. ACTA is in the works. SOPA isn’t really dead anyways
This will be a long fight, and I think the best way to fight it is to make sure that any politician that supports measures like this knows that such an action will make this their last term in office and wind up changing their mind and going with the will of the people they represent. I am not foolishly optimistic enough to believe that we could unite strongly enough to make that actually happen, but I can dream.