An experimental procedure for transmission X-ray ghost imaging using synchrotron light is presented. Hard X-rays from an undulator were divided by a beamsplitter to produce two copies of a speckled incident beam. Both beams were simultaneously measured on an indirect pixellated detector and the intensity correlation between the two copies was used to retrieve the ghost image of samples placed in one of the two beams, without measuring the samples directly. Aiming at future practical uses of X-ray ghost imaging, the authors discuss details regarding data acquisition, image reconstruction strategies and measure the point-spread function of the ghost-imaging system. This approach may become relevant for applications of ghost imaging with X-ray sources such as undulators in storage rings, free-electron lasers and lower-coherence laboratory facilities.