Transient absorption spectroscopy using soft X-ray coherent light sources as ultrafast probes holds significant potential applications in chemistry, biology, and materials science. This article presents the design of a transient absorption apparatus based on desktop soft X-ray light sources. A commercial femtosecond laser system (4.4 mJ, 25 fs, 800 nm, 1 kHz) drives an optical parametric amplifier, generating a 900 μJ, 28 fs, 1440 nm short-wavelength infrared (SWIR) pulse. This SWIR pulse is spectrally broadened and temporally compressed into a few-cycle pulse (400 μJ, 16.5 fs, 1530 nm) by a hollow-core fiber compressor. Then, few-cycle SWIR pulse drives the generation of attosecond soft X-ray high-order harmonic radiation, with the maximum photon energy extending into the water window region (>300 eV). The spectral resolution of the soft X-ray spectrometer is determined to be 334 meV at 243 eV. The remaining 800 nm pump pulse from the OPA system is combined with the high-order harmonic soft X-ray probe by using a hole mirror, forming a Mach-Zehnder interferometer with a time jitter of less than 10 fs during the one-hour data acquisition. This setup demonstrates the feasibility of performing time-resolved soft X-ray spectroscopy in a compact experimental configuration. Preliminary studies of transient absorption near the argon L-edge and carbon K-edge are conducted, demonstrating that this system can be used as a powerful tool for element-specific, time-resolved, and transition-channel-resolved investigations of electron dynamics.