Forward time travel is possible. Backward is not. Backward time travel cannot be achieved because of the creation of paradoxes. Forward time travel is possible, and the method of it is known, but not yet attainable with modern technology. You go as close to the speed of light as possible, but obviously not attaining it because that goes against the laws of physics, and basically the faster you go, the slower time goes by for you. So basically travel at this speed around the Earth for lets say 5 days, and stop in the same position as when you left, and you will have only aged 5 days, but return to Earth, and everyone will have aged 5 years for example. The reason you have to go so close to the speed of light, is because the effect of time moving slower is negligible at slower speeds, which is why someone traveling in a race car at 150 mph effectively ages the same as someone in the crowd spectating. Kind of off the topic, but to achieve such a speed, you would firstly need enough fuel to reach that speed, as well as slow down, because in the vacuum of space you need some sort of propulsion in the opposite direction being traveled, in order to slow down, because of the lack of a source of noticeable friction. Secondly, you would need to take into account the time needed to speed up, and eventually, in the process of speeding up, you will achieve a speed that has a noticeable shift in the speed that time goes by, so you would need to figure out the equation of exponential rise to pinpoint exactly when all of this needed to occur in order for you to reach your target destination.
...Or you could avoid all the hoopla and buy a DeLorean...