Here is how to use the tourism side of the Library of Congress: Go through the metal detector and put your belongings through a scanner ("there's a million nails in your boots!"), then walk through the exhibits (or use your wheelchair, or one of the available wheelchairs).
Here is how to use the Library as a library: From the tourism side, take an elevator to the cellar, then walk through a service tunnel to another building in the complex, take an elevator to the ground floor. In the card issuing room, present an id and confirm that you want the Reader Card for research rather than as a souvenir, which is forbidden. Take your new card back through the tunnel and up the elevator to sign into the computer room and present library card to the security guard- oops! No coats or bags are allowed! Back down the elevator to the coat check, then up to the computer room (can skip this step if you have the call number memorized or have looked it up in advance). Fill out a request form and hand it in in the Main Reading Room. Within 90 minutes, your book will arrive at your numbered wooden desk, unless the book is stored offsite. The reading materials can't leave the room, of course, but you can make photocopies.