How do we know that the Earth is divided into plates if we can not see them? What evidence is there?

There are several clues we used to deduce the plates. Among them are fossil evidence, the shapes of continents, ridges, and paleomagnitism. 

Fossil records on various continents would often show the same species of dinosaur. For example, Lystrosaurs were found on Antartica, Eurasia, India, and South Africa. These continents are now thousands of miles away from each other. Glossopteris fossils can be found on every continent, showing that at one time, they were all joined in...

There are several clues we used to deduce the plates. Among them are fossil evidence, the shapes of continents, ridges, and paleomagnitism. 

Fossil records on various continents would often show the same species of dinosaur. For example, Lystrosaurs were found on Antartica, Eurasia, India, and South Africa. These continents are now thousands of miles away from each other. Glossopteris fossils can be found on every continent, showing that at one time, they were all joined in Pangaea. 

If one were to take all of the continents and cut them out of a sheet of paper, one would find that they all fit closely into a single block. This supercontinent is called Pangaea. 

The mountain ridges on Earth are a puzzle when you try to explain their formation without tectonics. When the spreading of the sea floor was discovered, it showed that the plates needed a place to go. Subduction zones and ridges were the answer.

Paleomagnetism is the study of magnetic field orientation in cooled lavas. On the ocean floor, there are bands where the cooled lava shows earth's magnetic field pointing different directions. This is evidence of large scale change over time.