Time Travel

I'm working on a short story and want to use Time Travel as a way to tell it. The story does not revolve around time travel, but the characters will have to use it. So, how involved does one get in explaining the intricacies of something that is so thoroughly hypothetical? I've always felt that one doesn't necessarily explain the Macguffin. If a story calls for vampires, then the story takes place on a 'hellmouth', if you have to go back into time to rescue humpback whales, then you slingshot around the sun; and of course if you are Superman you can just make stuff up.

More important is to stick to a set of rules when time traveling. But what are those rules and are they universal? The Terminator can't travel through time with anything synthetic(on the outside). It's a strict rule that makes for an interesting opening. However, how in the frick does one follow the logic of what happens afterwards? (spoiler) I'm John Conner, and I sent my father back into time to sleep with my mom, get her pregnant with me and raise me to be me. Of course, I can't have actually done that, because I don't exist as of yet.

And consider this: what if the terminator DID actually kill the correct Sarah Connor? What if, as a result of her encounter with the terminator, the incorrect Sarah Conner names her son John and trains him to be a John Conner of the resistance, but not THE John Connor?

How much sense does time travel have to make, and at what point do you just start scratching your head? Consider this website on temporal anomalies in time travel that made me wonder: http://www.mjyoung.net/time/index.htm

If the story is good, can the time travel be bad?