Caution: Long post below. Read only in the presence of ample time.

It is relatively more difficult to prove that time travel is not possible than to prove that it is possible. Before I move on to the idea of How, I will try to prove the possibility of the radical concept of twisting our fourth dimension.

Consider Einstein’s theory of relativity. The main drawback of this excellent theory is that it does not apply to light. Not because the velocity of light makes all velocities negligible, but because the speed of light is a rigid constant – both actual as well as apparent velocity will remain the same, at the cost of either distance or time.

What I mean to say is, the relative movement between the source and the observer has no observed effect on the velocity of light, or the time it takes to reach a certain spot. Even if the relative velocity is comparable to the speed of light, it shall have no effect (this is a proven experimental fact, do not bug me with questions about this, I simply do not know).

(One thing you should know is that even though the velocity is unmodified, the wavelength and frequency of light are modified, hence giving birth to Red Shift [Blue Shift is very rare] – Read about this somewhere else, I haven’t got the time. Besides, Its unrelated.)

This means that the rigidity of the speed of light actually modifies the perception of time. Don’t get it? Let me explain. The speed of light turns out to be exactly the same for both the source and the observer moving relative to the source, because time, as measured by your watch, ticked along at a slower pace than time measured by the observer.

Thus, I have proved that time can slow down or speed up for someone in particular cases. Time travel, thus, is possible. Now for the question of how.

I will now make a point which might make me the enemy of all astronomers and physicits on Earth. It is possible to travel faster than light. Or at least make it appear so. Let me give you a silly and unrelated example to prove this beyond doubt:- In a race between two cyclists A and B, the objective is to complete a lap around a circular track. There is a path in the diameter of the track, not known to cyclist B but used by cyclist A. As A uses the path every time and B has to travel all the way around, it will appear to B that A is moving much faster, even when he isn’t. Similarly, the universe has many such “short-cut” paths known as wormholes. The use of these wormholes might just enable time travel, by changing how it is perceived by different people. If an hour to you is a second to me, I have succesfully travelled 3599 seconds forward in time.

Now, I cannot stress this enough – It is NOT possible to travel back in time. At the very max, as in the above example, a second for someone can be an hour to you, wherein you have slowed time down, BUT, you CANNOT REVERSE IT. A new born baby is not going to go back in the mother’s womb, so to say, because we are limited to modifying perceptions, not dimensions.

Also please note that actual movement at the speed of light will convert all the matter in your body into energy (according to one really bothersome formula, mass will become infinte. In order to accelerate infinite mass you need more than infinite force, hence travel @ the speed of light is impossible) , it is inadvisable to try to acheive such speed. Just “make it appear so” with the help of wormholes (see P.S.) or something.

The Lame Way
Another possible way (and it is the lame way) of travelling in time is to consider time as being defined alongwith light. The time on Earth, for example, is timed according to the rotation of the planet, as compared with light from the sun. (Otherwise we would not be able to see anything, so there wouldn’t be much to compare our own motion with, Earth would just be a something doing something in the dark). Then, we divide Earth into time zones, and travelling from one zone to another at a velocity faster than the Earth’s speed of rotation, we do time travel! And its not much use because one second is still one second and there’s no fun in that.

P.S.> On Wormholes
It is unknown whether (Lorentzian) wormholes are possible or not within the framework of general relativity. Most known solutions of general relativity which allow for wormholes require the existence of exotic matter, a theoretical substance which has negative energy density. However, it has not been mathematically proven that this is an absolute requirement for wormholes, nor has it been established that exotic matter cannot exist.

P.P.S>Utter Bullshit
Backward time travel through a wormhole could be accomplished by accelerating one end of the wormhole relative to the other, and then sometime later bringing it back; the modification of time perception would result in less time having passed for the accelerated wormhole mouth compared with the stationary one, meaning that anything which entered the stationary wormhole mouth would exit the accelerated one at a point in time prior to its entry. The path through such a wormhole is called a closed timelike curve, and a wormhole with this property is sometimes referred to as a “timehole.”