I have headed up internal audit in both corporations and charities. The IIA standards for the practice of internal auditing apply equally well. You can see them at the link below.
Not all charities have an internal audit function, but many do and I know from experience that some large charities outsource their internal audit to private firms. Normal standards apply.
All charitable entities have operation function in whatever form or name it is called. Internal audit function is handy to provide independent and objective assurance and sometime consulting services on whether the said operation function is achieving its objectives. This could be outsourced as observed by Lynn.
Most of the generally accepted auditing standards apply to charity organizations. Therefore, most of these organizations, especially the fair-in-size ones, have internal auditors and sometimes have full-bodied audit departments.