I got a request to do this and I listen to the people!
Firstly, time travel backwards is generally accepted as impossible. Excluding the fact the object being transported (you) has mass, light speed is the cosmic speed limit. To go backwards in time you need to go faster than light or use something like a worm hole. Worm holes do exist, but they are smaller than a single atom. Expanding them through some futuristic technique may be possible, but their existence will be ended almost immediately by (it is thought by people such as Steven Hawking) radiation feedback. That is, radiation going through the worm hole, out the other side, and back through over and over again till it builds up sufficiently largely to destroy the worm hole. A similar concept is that screeching sound from amps you get when sound is going through the microphone and projected by the speakers so loudly that it is again being picked up by the microphone and projected a second time.
Time travel into the future is allowed for, however, and has even been done, albeit not very far. There are two ways to do it from Einstein's theories of relativity. One is via the mass of another much more massive object and the other is via velocity. Using the first method, an extremely large mass would be required, such as a black hole. If one were inside a ship on the edge of the event horizon of a black hole, time dilation would occur. Not only would this be extremely dangerous, the outcome is theoretically about only 4 seconds of time per second into the future (so 1 year around the black hole = 4 years on earth).
The second option is via a large amount of velocity. This is the best hope for traveling into the future. If a ship could get to 99.9% of the speed of light, which may be possible in the future, hundreds of years would pass on earth for every 1 year on board the vessel. Interestingly, Hawking explained that a ship such as this would take about 6 years to get up to speed. What he didn't say is that it completely depends on the mass of the ship itself and the amount of power moving it. If the ship were much less massive, it would take much less time to accelerate to speed. Essentially, his calculation is meaningless. We have no idea how massive such an object would be, nor the amount of power possible to get out of it. Sergei Avdeyev has traveled about 20 milliseconds into the future from his extremely long stay on the Mir space station.
I would have to recommend cryogenics as the only method of 'time travel' for the immediate future. Of course, once you are frozen you cannot be woken until that little detail is figured out :)
Comments welcome as always!