This illustration represents Pangaea, the supercontinent that existed about 225 million years ago, a time when the dinosaurs were first establishing themselves as a life form on Earth.  The colored regions reveal regions of present day continents were fossils of the indicated plant or animal were found.  Thus, fossils of the fern, Glossopteris were found in all of the continents shown above.
How could they have traveled so far?
Why of course, they never traveled at all.  Instead, the continents moved carrying the fossils.

This map reveals the supercontinent Pangaea. At this time, all of the modern day continents resides close to one another and plants and animals were moved freely over all of the continents.

During the Triassic, when the dinosaurs were on the ascendency, Pangaea had broken into two large landmasses: Laurasia to the North and Gondwanaland to the South.  Note the existence of the Thethys Sea that nearly separated these landmasses.

During the Jurassic, when the dinosaurs ruled Earth, the Thethys Sea had nearly separated the two continents.  Note that present day North America and Europe are discernible parts of Eurasia and South America, Africa, India, Antartica, and Australia are beginning to take on individual shape.

It is the Cretaceous and the dinosaurs have passed from the scene-making possible the asdency of the mammal.  The modern day continents are much more easily seen and you should be able to identity all of the major landmasses in the above map.

Is this the end of the story?  Will the continents remain in their present day position forever or are they mutable?