Time travel is probably the most revisited speculative fiction trope. Whether we as writers--or our characters as characters--are driven by guilt, greed, bloodlust, or just the compulsion to throw a wrench in the temporal machinery and see what happens, there always seems to be a good reason to travel through time.
Putting aisde the temporally anomalous heebie-jeebies that our characters and our make-believe universe must undergo whenever we resort to this mechanism, writing time travel can create many sticky situations for the writer. To produce a reliable narrative that the reader won't (immediately) scoff at, there are two things a writer must do.
Firstly, lay the ground rules governing the physical reality of time travel. Can the time-traveler physically exist in two times, or does the mechanism (scientific, magical, or otherwise) merely transport the "consciousness" or "mental state" of the individual into an "earlier" body? Is the mechanism a crystal ball, letting us see things, or a teleporter, letting us touch them? Can the traveller go forward, backward, or both?
For some writers, addressing these questions might be the bulk of the work. But in writing speculative fiction--and writing it with the intent to produce a feasible story--it is at least, if not more, important to take the second step: comb your time-travelling tale for cohesion and consistency. Time-travelling isn't like the process for forging steel, or the season in which a certain flower blooms: there is no bank of truly irrefutable facts on time-travelling, no empirical evidence with which we must comply. Thus, time-travelling in fiction will create the same challenges for a writer as creating a magic system. Securing belief in it hinges on the consistent application of its internal rules to the chain of cause and effect, and the degree to which those effects cohere to their causes, scattered back and forth throughout time.
In other words, the literary effectiveness of a time-travelling mechanism--the degree to which the reader will be satisfied--is one hundred percent the responsibility of the writer.
So, how can you ensure the literary effectiveness--the consistency and cohesion--of your time-travelling mechanism? Despite the great loops, warps, and anomalies that time travelling can create, and the conconmitant loops, warps and anomalies that might arise in the frustratedly logic-thirsty brain, writers in this day and age have the advantage of word processing software. Regardless of specifically how your time-travelling device works, it will inevitably impose curious cause-and-effect chains that you, as a writer, must prepare for--and possibly contort your story to obey. But when the story is complete--when all the time travelling has been said and done--it is no more difficult to "fact check" your story than to cut-and-paste the scenes and paragraphs into consecutive temporal order. Regardless of the way the story is ultimately told, the way the story occurs for its characters must be thoroughly rational, causal, and orderly. If a reader were to do the exact same thing, cutting your story into its corresponding parts and fitting them together from temporal point A to temporal point Z, they ought to see all the nuts and bolts slide together.
Putting your story in temporal order, and rearranging it later to create the drama and suspense, is the perfect way to ensure that there are no wrinkles in your time-travelling mechanism.