The key to plotting satisfying time travel stories is to make sure you keep them grounded in satisfying story arcs. For all its complication, Interstellar is a story of one father’s love for his daughter. Groundhog Day is about making the most of a day, and finding what’s important. Back to the Future follows science-based MacGuffin action-adventure plotline, and so on.
Once you have a framework in place for the story you want to tell, search for logical paradoxes. Remember, motivation is a key factor in whether you cause a paradox in even the most grounded of stories. You can also embrace the ‘many worlds’ theory and accept that the new timeline takes place in another universe. Either way, once the coast is clear, you want to explain your system, but always show, don’t tell. Like we mentioned about Back to the Future, burying the explanation in the dialogue is a great way to keep things moving along without losing your audience, but don’t spoon-feed walls of text, either. Less is always more, and KISS (Keep It Simple, Stupid) are your buddies here.
Armed with that knowledge, do yourself a huge favor and chart out a timeline. This will help you to stay on track and spot paradoxes as they crop up. The more complex the timeline, the more you need to hand-hold your audience and walk them through it (re-watch Back to the Future 2 with this in mind and you’ll see it in the dialogue.)
Now, have fun and get crafting.