During the Meiji period, the reformers were able to achieve rapid industrialization in two major ways.
First, they set up an environment in the country that was favorable for business and economic growth. They did this by such things as removing restrictions on trade within the country (things like restrictions on who could conduct various kinds of business) and by assuring internal stability (preventing wars or rebellions).
Secondly, the government took a much more direct role in the economy. They actually helped to develop certain industries by funding research or by giving aid to companies that were involved in important new industries.
Of course, it was not just the government reformers who helped Japan industrialize. It was very important that there were many private individuals who stepped forward to create new businesses. These were the people who actually made the economy industrialize, though they did so with a great deal of help from the government.