There were a number of steps taken by the various Axis powers to make themselves more powerful in the years before WWII. The most prominent of these were their military incursions into foreign countries. All three of the main Axis powers took such steps.
All of the Axis countries wanted to have more territory and more power. Japan invaded Manchuria and then China in an attempt to get more of an empire. Italy invaded Ethiopia. Germany took Austria (Austria more or less consented) and then took first part and then all of Czechoslovakia. Germany also participated to some degree in the Spanish Civil War. This gave its military (particularly its air force and navy) a chance to get more experience.
Germany also took other actions because it was the only one of the Axis powers to have been defeated in WWI. Therefore, it, unlike Italy and Japan, had to secretly rebuild its military. It also had to make diplomatic arrangements, particularly with the Soviet Union, to allow it to rebuild economically and militarily.
So, the three Axis powers did various things to become world powers, but the most prominent steps they took were military invasions.