The simplest version has a young scientist being visited by an old man from the future. The old man has a dying time machine and needs the young scientist's help in repairing it. This he does, but before the old man takes off, the scientist (excited by a real-life time machine) tries to take the blueprints for it. The old man stops him, but only manages to grab half as he goes back (presumably) to the future. The young scientist, left with only half of the plans dedicates the rest of his life to accomplish time travel, and with half of the amazing technology in hand he feels confident he will achieve it. Fast forward, the scientist who is no longer young, is very old, but is about to complete his time machine. He tries it out, and it works! But something goes wrong, he is too old to fix it now and the only person who is smart enough to help him is a younger version of himself. He visits his young self and together they repair the machine. The old man is about to take off when his young self tries to take the blueprints for the time machine. His young self manages to grab half as the old man zips back to the future. The old man now realizes that the old man he saw from the future when he was younger was himself. Checking the old half blueprint he grabbed from back them perfectly matches the rip in the half he is left with now. But how can that be? Where did the technology from the time-travel come from? Where did the idea for time-travel come from? Not from himself, it was the old guy and the old guy's technology that did it. But he is the old guy!
Basically, if you think about logically, the story is impossible. It has no beginning and no end. That is what makes it a logical paradox. The circular time-travel theory is fun, but has no bearing on reality as its basic premise is to viloate and cicumvent cause and effect.
T2 is a whole other story. It follows the branching Time-travel theory or multiple Time-line history theory. In T2, you can go back in time and mess with everything as this will change the future and create a new branch in history, meaning history would have originally went one way, but because you changed it, it will now go another way. Or with multiple Time-lines, every change to history you make creates another time line and that is the one you are currently in (the other older time-line still exists, but you're not in it anymore. With this theory rather than changing history around you, it is you moving from one time-line to the next).
With T3, ehh. T3 was mostly a comedy. It doesn't take the sci-fi stuff seriously.