Start with the Website
If you want a couple good primary indicators of a charities legitimacy as a reputable organization take a good look at how they handle transparency and accountability to the public.
A good place to begin is with a solid professional website. Any organization that hopes to garner interest from the public sector must have a well-conceived and informative primary touch point. the next course of action is to peruse the quality of the information. Are they providing you with facts and figures that represent the true fundamentals of the respective organization soliciting your donations? You should be able to easily navigate the site to find information about most any aspect of the charity you wish to gain more knowledge about.
It can take a bit of time to become proficient at recognizing if a charitable organization is being resoundingly transparent and accountable for the material they are putting out there. Simply comparing sites of highly regarded charity organizations is a nice place to start for those of you who are beginners. You will quickly begin being able to discern between good and sketchy practices. A couple things to keep in mind are of course full disclosure of all or most financial information and you should be able to find out as much as you want about the people that run the organization along with their history of accomplishments both inside and outside the organization. As always the Charities Form 990 is an excellent resource for culling the relevant information behind the charity.
Scott Davis offers charity insights for all levels of experienced givers