“Authorized shares” refers to the number of shares the corporation is allowed to issue under its certificate or articles of incorporation. 10 to 15 million is a commonly used range (we set 10 million as default for the Cooley GO Docs Incorporation Package).
You can find the balance sheet in its annual report or in any of its quarterly reports. Locate the stockholders' equity section, which is toward the bottom of the balance sheet. There should be a "common stock" section, which can tell you the number of issued shares as well as the number of authorized shares.