Dusty, star-forming galaxies and active galactic nuclei that contribute to the integrated background intensity at far-infrared wavelengths trace the large-scale structure. Below the point-source detection limit, correlations in the large-scale structure lead to clustered anisotropies in the unresolved component of the far-infrared background (FIRB). The angular power spectrum of the FIRB anisotropies could be measured in large-area surveys with the Spectral and Photometric Imaging Receiver (SPIRE) on the upcoming Herschel Space Observatory. To study statistical properties of these anisotropies, the confusion from foreground Galactic dust emission needs to be reduced, even in the "cleanest" regions of the sky. The multifrequency coverage of SPIRE allows the foreground dust to be partly separated from the extragalactic background, composed of dusty star-forming galaxies as well as faint normal galaxies. The separation improves for fields with sizes greater than a few hundred square degrees and when combined with Planck data. We show that an area of ~400 deg² observed for about 1000 hr with Herschel SPIRE and complemented by Planck provides maximal information on the anisotropy power spectrum. We discuss the scientific studies that can be done with measurements of the unresolved FIRB anisotropies, including a determination of the large-scale bias and the small-scale halo occupation distribution of FIRB sources with fluxes below the point-source detection level.