How much of the company does one need to own in order to replace management/board of directors?

Usually, controlling 51% of the existing capital stock would do the trick. The next step is to preserve that percentage of ownership until the next stockholder's meeting. In the stockholder's meeting, usually held at a particular date each year as stated in the Articles of Incorporation or By-Laws, a new set of Board of Directors is elected. If you own 51% of total voting shares, you can replace all of the members of the Board with persons of your choice. Once you have a Board of your choice, you control the corporation.