Unfortunately, you can't visit the interior of the building. I was exploring the website recommended by Missjef while she was posting the link. If you check 'Factfile > FAQ', you'll see that you can access the plaza and Arcadian Garden but not the office block itself. With current security concerns for financial institutions in London, it's probably unlikely that any members of the public (other, possibly, than bona fide students of architecture on a visit arranged by their university) would be allowed any form of access.
Chris
PS: I see that Norman is as accurate as ever. He's managed to post a completely irrelevant statement (because the Gherkin isn't a museum) which is incorrect anyway. (Only the major national museums are free. Many others still charge for admission).