It is possible to time travel into the future; however, travel into the past is not generally accepted, although some theories do indicate a possibility (via "womholes'). For travel into the future, all you need to do is leave earth in a spaceship and travel at near the speed of light for a while. When you come back, the earth will be older than when you left my more than the time (you measured) to take your trip.
Right now as far as the public knows there is not but there are to many theories on how to do it to explain. The simplest is you build a train track around the world with a train tht goes as close to the speed of light as possible. You put people in the train and send it around the earth for 50 years. The train loops the planet I think it was 186 times a second for 50 years. When the train stops after 50 years the people I side would have only aged 25 years because since they are inside the the train time is essentially slowed down from the speed. So those people went into the future in something that seemed like a few hours and only aged 25 years in 50. It is the easiest to grasp but one of the most costly and dangours
Into the future, technically yes. Into the past, no.
For the future, you can use this method: according to Einstein's theory of relativity, time slows down when you speed up. For most situations, the effect is negligibly small, but at high speeds (as in, close to the speed of light), it is noticeable. Now, you can use this to effectively slow down time for yourself, thereby travelling into the future. For instance, suppose you got in your spaceship and went close to the speed of light, and kept that speed up until you'd spend 10 years on the ship. When you landed on Earth, you'd find that a lot longer time had passed, say 100 years. This effect has been confirmed by experiments with very precise atomic clocks, but apart from that, it's very difficult to get up to the speeds necessary to use it for anything useful.
For the past, there is currently no known method by which we can do this- as far as we know, sending information of any kind into the past seems impossible (which automatically invalidates sending anything else into the past as well). There is the occasional theoretical proposal, but usually they don't hold up to detailed analysis, and so far none has ever been validated.
I actually watched a documentary on this not too long ago. From what i understand you would have to travel away from the earth very very fast (speed of light fast) for a while (couldnt give you an exact time) and then travel back to the earth at the same speed. Some how, dont ask me how, the extreme speed and distance affects the "time" and you would litterally be in the future when you land. How far in the future and exactly why this works is completely beyond me.