Note: It's a good idea to do a trademark search even before you register your domain name, since domain registrars are not obligated to check if a requested name violates an existing trademark.
Fill out an application. There are three ways to apply for a U.S. trademark: one for applicants who have already used the mark in commerce (a "use" application); a second for those who haven't yet used a mark in commerce but intend to do so (an "intent-to-use" application); and a third for applicants who live outside the United States and have registered the mark in another country. You can fill out any of these applications, check them for completeness and submit them over the Internet through the USPTO's Trademark Electronic Application System.