Nauta said he also advises checking for pending lawsuits against the charity. Many states provide free online access to court records. While a lawsuit is not proof that a charity is doing something nefarious, it might give a donor pause.
Additionally, most nonprofits—excluding churches—are required to file a Form 990 yearly with the Internal Revenue Service. (Those with less than $200,000 in annual revenue can file a simplified form.)
The form includes broad financial disclosures and must be made available to anyone requesting it. Many charities post the form on their websites. However, it can often take up to a year after the group's fiscal year-end for the 990 form to be available.
Read MoreTop 10 investment scams
However, CharityWatch's Borochoff said that some information in the form can be vague, especially when it comes to in-kind gifts (anything besides cash) made by the charity.
"It could say they're sending medicine and medical supplies worth $1 million somewhere overseas, but it doesn't give you a really clear idea of exactly what they're giving," Borochoff said. "Sometimes there have been cases where the value of such [in-kind gifts] are wildly inflated."
Once you've checked the watchdog websites and the charity's Form 990, advisors recommend looking into the governance and oversight of the group. Start by looking at the board of directors.