The Smithsonian has a fun article about time machines.
A physical time machine—a device available at Wal-Mart, as opposed to a natural wormhole somewhere in the cosmos—is possible. You begin with something square. Next, install mirrors at the corners and send a beam of light, perhaps from a laser, at one of the mirrors. The light will bounce to the second mirror, the third, the fourth and back through this cycle forever.
The force of this constantly circulating light will begin twisting the empty space in the middle. Einstein's theory of relativity dictates that everything happening to space must happen to time, so time begins twisting, too.
To fit a human inside this time machine we need to stack a bunch of these mirrors on top of each other, and add more light beams. Eventually, we'll have a cylinder of circulating light. Once we step inside, we're ready to fly through time….
Here's the catch: The time machine only allows someone to travel as far back as when the machine was first activated. Since no time traveler has shown up yet—check-out aisle tabloids notwithstanding—no such machine has yet been invented.
In January, This American Life featured a terrific story about a physicist named Ronald Mallett who had spent five decades trying to make a time machine to visit his dead father. Mallett wrote a book about his quest, called Time Traveler: A Scientist's Personal Mission to Make Time Travel a Reality.