Using a hydrodynamic simulation of a cold dark matter universe with a cosmological constant, we investigate the X-ray forest absorption imprinted on the spectra of background quasars by the intervening intergalactic medium (IGM), at redshift z 0. In agreement with previous studies, we find that O VII and O VIII produce the strongest absorption features. The strong oxygen absorbers that might be detectable with Chandra or XMM-Newton arise in gas with T ~ 105.5-106.5 K and overdensities δ 100 that are characteristic of galaxy groups. Future X-ray missions could detect weaker oxygen absorption produced by gas with a wider range of temperatures and the lower densities of unvirialized structures; they could also detect X-ray forest absorption by carbon, nitrogen, neon, iron, and possibly silicon. If the IGM metallicity is Z = 0.1 Z, as we assume in most of our calculations, then the predicted number of systems strong enough for a ~5 σ detection with Chandra or XMM-Newton is extremely low. However, scatter in metallicity increases the number of strong absorbers even if the mean metallicity remains the same, making the predictions somewhat more optimistic. Our simulation reproduces the high observed incidence of O VI (λλ1032, 1038) absorbers, and the most promising strategy for finding the X-ray forest is to search at the redshifts of known O VI systems, thus reducing the signal-to-noise ratio threshold required for a significant detection. However, while many O VI absorbers have associated O VII or O VIII absorption, the O VI systems trace only the low-temperature phases of the X-ray forest, and a full accounting of the strong O VII and O VIII systems will require a mission with the anticipated capabilities of Constellation-X. The large effective area of the XEUS satellite would make it an extremely powerful instrument for studying the IGM, measuring X-ray forest absorption by a variety of elements, and revealing the shock-heated filaments that may be an important reservoir of cosmic baryons