The title of this node is only partially correct. Time travel into the past is impossible without resorting to highly speculative wormholes and related celestial bodies. Time travel into the future (meaning progress into the future at an accelerated rate, not just strolling into the future at a 1:1 ratio, as it is now) is quite possible, using only the power of engineering. If one could build a spacecraft that could go very close to the speed of light (90% or higher), the ratio of time passed on Earth to that passed in the craft will become noticeably higher, in accordance with the Special Theory of Relativity. This effect is called time dilation.
The formula that determines the ratio is as follows:
sqrt(1-(V^2)/(C^2))
(V is velocity, and C is the speed of light. Using SI units is not necessary, but the units must match.)
You will get a decimal answer. This decimal indicates the lower time passed in the craft. For example, if you get an answer of 0.25, that means that 0.25 years will pass in the craft for every 1 year that passes on Earth.