You guy's already know what time-travel basically is so I'll just get to the main point: Time travel is only complicated the more you try to micromanage the events that happened as a result of time travel.

In time loops, the focus is usually put more on seeing new sides to people and what they would have done if your specific actions were different. I can reference just about a dozen stories with either time travel used to send the protagonist into a foreign or ancient world and even The Melancholy of Haruhi Our Great God had a time loop that made the audience watch the same events multiple times.

Just go see the movie and you'll catch my drift. It will be too boring to explain this trope through examples so I'll spice things up by taking a step back. Let me explain my own personal thoughts on this first:

In my perspective: There are two kinds of forces that can affect events in time travel stories. The first being the intentions of the characters while the second being the natural world around them.

Let's say you're trying to save someone from an accident involving the weather in the past. Perhaps getting them to a safe zone or something wouldn't really affect the wider world as a whole. However, it is up to the author if events happen 'because the of the main character' or 'because he used a very unstable time machine that messed up time'.

I feel it's best to explain this first since it doesn't seem convincing if the main problem to your story isn't the change of events but because of an external interference messing your happy ending.

Things like: 'You have messed up fate and now this person is destined to die' only work if you are being aware that he isn't ACTUALLY at fault for the mess that's made. It's just Lady Time screwing him back.

This kind of thing is usually made for stories that show the dangers of trying to mess with a fundamental concept of reality. In other words: If you want to be happy, don't screw with time travel.

Messing with it causes time loops, paradoxes with your mom, and other horrific things that can only be fixed once you've either learned your lesson and stop messing with it any further than 'the incident'.

Of course, there are also stories where time travel itself doesn't have any disadvantages and it's the decision made by going back time that make things suck. This is not to be confused with 'you stepped on a leaf and now the future sucks', the change I'm referring to is mostly to do with how you changed interactions with other people that made them do something they didn't do in the previous timeline.

While it's not uncommon to have your main character step on a twig or something that causes a dog to wake up or something. If it's just you being there that messes with the wider world, then that attributes to previous point of angering Lady Time.

You would find it extremely confusing to write a story that involves time travel mechanics. However, there is a simple solution to making it easier, and that's by understanding the 'determinism' intrinsic to this specific trope: Why is the past always the same?

To explain: Determinism is to say that a person is defined by their past and their future actions are also a result of the past. The reason kid shows can easily add time travel is because they don't try to add layers to fictional characters like writers do.

Who can argue if I say another person changing the past to take that toy car I loved as a kid didn't turn me into evil mastermind? Basically, the reason you can even go back in time in the first place is because past events are 'determined' to happen due to events prior leading up to it. Changing something might not change the entire story, but it will at least leave behind evidence that you were actually there.

Okay, I'll finally give some examples now. You know in Doctor Who where he goes back in time and the only change to the future is someone remembering a big blue police box? It's a little like that, not all actions really need to change anything, since it's hard stopping events that are fully 'determined'.

Different problems in the past require different solutions whether it be needing to stop someone they really WANT to do, making a mistake out of unstable emotions, or just stopping them from being crushed by a tree that happened to fall on them.

If your character goes on a evil power trip saying that he's the lord of time because he can time travel then the reason he'll most likely be proven wrong is due to the inherent 'smallness' of one person overall.

Even if you wanted to stop Neil Armstrong from stepping on the moon, there's literally nothing you can do about it if you're just some normal guy who cannot influence people of greater stature.

If you try raiding NASA, you get turned into a sieve by bullets. If you try speaking out, there is no way these learned people would listen to the words of a plucky teenager who says he's from the future.

This is why time travel stories like Stein's Gate are so character driven. After all, if you already know these people, then there's a greater chance of persuading them NOT to do something that messes the future.

However, this is all me assuming that your main character is the one time travelling. If it is given to a side character instead then this trope can be twisted into truly unique stories where despite the main character not being in the know initially, a whole mystery can be uncovered through slowly giving out information that suggests a unnatural phenomenon.

Now I've said enough about 'going into the past' already. Now let's talk about the future. Let me get one thing out of the way first: There are zero disadvantages to travelling into a time where you're already dead and they can't 'travel back' to arrest you because of something stupid like wearing ancient clothing in this world where everyone specifically wears the exact same outfit. 

However, if you are actually interacting with your future self, then the timeline will already be changing ever so slightly. There's this Manga called Time Lover (I think) where the main character was accidentally getting phone calls from her deceased lover, this phone call being way back in the past.

In this story, the initiator of the paradox isn't her but someone relevant to her from the past, and the only way to save her lover and change her 'present' is to figure out who was responsible for killing him.

Now this was a highly specific example I gave but you get the gist of it, right? The who shtick of paradoxes and time loops is that the audience and protagonist actually need to search for the solution of how to fix their problem and actually getting it done. In the moments before these two goals are achieved, it is just used to characterise the main cast since I wouldn't read about people I don't like.

Oh yeah, there was thing time travel stories do a lot which demands the main character to not meet himself or the world will end or something, but that kinda thing isn't required. Just like I was saying with my first point, how time travel affects reality is up to your imagination. I mean, all you'd really think if someone looking like yourself came up to you would be: "Isn't this guy incredibly handsome?"

That's all I got, thanks for reading~!