The SOPA was written to address "US-based interests", i.e. it specifically claims to go after only US-directed foreign websites, to prevent US-based people from seeing those foreign websites.
(Defn: "US-directed" means that the site hasn't taken steps to prevent US people from seeing the website, or other nonspecified reasons. "Foreign website" means a domain name which is registered by a non-US registrar, or an IP address which comes from a non-US block).
But the US doesn't have jurisdiction over foreign domains/websites. So, in that absence, it's US-based companies who have to act:
* US-based ISPs have to take measures to prevent their customers from "accessing" those websites 5 days. It's not clear what measures must be taken, but they include at a minimum blocking DNS lookups.
* US-based search engines have to remove hyperlinks to those foreign domains/websites within 5 days
* US-based ad brokers have to cease serving ads to those foreign domains/websites within 5 days
* US-based payment companies have to cease processing payments for those foreign domains/websites with 5 days
Moreover, any US-based service which bypasses this censorship -- TOR, Mafiaafire, free and open DNS servers -- will be shut down by the courts.