If you think an organization may be a non-profit, go to their website and look at their mission, core values, or strategic plan. Try to determine their purpose. Are they looking to gain stockholders or save the environment? The language in which they use should be the first indicator of their purpose.
Next, look to see if they provide financial reporting. Many non-profits proclaim themselves as a 501(c)(3) public charity on their websites and link to their financial statements. They may also have links for you to donate and how to claim that donation on your taxes for a charity benefit.
Finally look for the accountability information in the form of Annual Reports or other documents that report that may include: what they've done with donated earnings, their initiatives or research, what they have accomplished, who their corporate sponsors, partners, or donors are, who they've helped, members of leadership, and/or future initiatives.
Many times, you can search for non-profits using popular search engines, however there are dedicated websites that display non-profits if you do not want to take the time to research if an organization is actually a non-profit or not.