Although all sceintists do not, or did not, use the same methods to make their scientific discoveries all have some common characteristics. These two methods are the most representative: 

• The experimental or inductive method 

This is the most used way and is developed more completely in this topic.  
When we are children we learn like this: when we observe something our sensors (senses) send the impulses which are created to the cerebral cortex (a fine layer of neurons which covers the brains of mammals and which formed a million years ago) and this is where our image of the world is created and we make our predictions about how it works. By testing our predictions we shape and improve our image of the world.  

The scientist, either because he or she wants to understand a phenomenon which has not yet been explained, or to further develop a determined process, carries out experiments with the phenomenon under study varying the variables involved one by one until he or she can INDUCE a law which relates them.  The induced law, to be verified, must always apply. This is how the hypotheses formed are confirmed.

This method induces us to discover a Theory by means of experiments. 
Carry out this activity - an example of an inductive process.

• The theoretical or deductive theory 

Newton used this method to develop the theory of Universal Gravitation. 
Einstein used this deductive method  to develop the Theory of Relativity.