In the previous article by Jianchen, we examined the possibility of time travel, and the many paradoxes that crop up when you attempt it. All of it sounds quite mysterious and if you haven't read that piece, you should do so now. Seriously, click here and go.

Now, assuming you've read the previous article, your brain is now a puddle of goo. Considering the implications of altered histories and fractured self-terminating timelines can be a mind-warbling exercise. But luckily for us, we have a tool that allows up to examine every idea and determine the truth.
Let's go.... SCIENCE!

So what do the laws of physics say about time travel?
In a massive surprise, the laws of science (as we know them today) do not prohibit time travel!
But there is one major caveat. You can only travel to the future, not the past (No killing Hitler yet).

But how? This is actually a property of the (almost magical) theory of Relativity, proposed by the (one and only) Albert Einstein. Henry Reich of the popular YouTube channel Minutephysics gives a nice small introduction to ways to time travel.
(For those who like reading more than listening, here's a text link to Wikipedia on the subject).

So let's examine those methods in a little more detail:

Do nothing
We are all travelling into the future at the fairly average rate of one second per second, so it should stand to reason that we are all time travellers. But we want to be special time travellers, don't we? So let's move on to;
Start moving
Now here's where it get's a little trickier.
In the theory of Special Relativity, we first figure out that things like distance and time are not absolute (i.e There is no universal time). Durations and distances are different for everyone and depend on your point of view (a.k.a. the observer's reference frame), but certain things are constant for everyone (like the velocity of light). Using this we come to the conclusion that what we consider time and what we consider space are not different things. They are just two components of the same spacetime, and are interchangeable, depending on the observer's motion. (If your mind is a puddle of goo now, I'm sorry. Special relativity wasn't understood in a day. If you really want to dig deeper, I'd recommend reading the book "Einstein For Everyone")
Summarising, you can exploit this theory to move faster in time, relative to someone else (which is what you wanted). But to have any significant change, like days or years, you'd have to go near the speed of light, which at 300,000,000 m/s or 1,080,000,000 (1 billion) km/h, is fast. Extremely fast.
So then let's try;
Go up
Here we encounter Einstein's other famous theory of General Relativity. This deals how gravity affects spacetime. If you thought Special Relativity was confusing, this is downright obtuse. (Link for the interested). For now, you'll just have to believe me when I say that gravity makes time slow down.
So you go up to the next floor. When you do this, the pull of gravity on you is slightly less than someone at a lower level, so time passes slightly slower for you than it does for the other person. But again, to have a real noticible difference, you'd need a body with far greater gravitational pull than the Earth can provide, so;
5. & 6. (Hypothetical) Rotating Universes, Infinitely Long Super-dense Spinning Cylinders and Wormholes
All these "techniques" exploit the fact that gravity bends spacetime and use it to bend so that it runs into another place (in time). The only problem is that 1) Our Universe is not rotating 2) These contraptions require types of energy and matter that are just hypothetical ideas with no evidence. So until we get some of that, there's not much to do here.

So, if you want to time travel, you can. But only very little, unless you're very fast, or very high up.