(covers information from several alternate timelines)
The design of the Walker class consisted of a saucer section with an integrated, laterally-positioned navigational deflector, a compact secondary hull, and two nacelles attached by pylons extending beneath the ship's superstructure.
The Walker class had at least fifteen decks and two shuttlebays. It carried a compliment of shuttlecraft and worker bees, as well as escape pods which could be launched from breakaway panels lining the top of the saucer section.
This ship class was capable of atmospheric flight by means of thrusters scattered over its ventral hull. The ship's armament included phase cannons, phasers, and photon torpedoes. The ship was equipped with internal and external plasmatic filters.
Atypically for a Starfleet vessel, the bridge was located on the underside of the saucer, on deck seven, and had an adjacent captain's ready room. The internal arrangement of the Walker class did not change significantly by the development of the more advanced Crossfield-class ships, with nearly identical corridors and crew quarters. The Walker class possessed transporter systems similar to that of the Crossfield-class; however, it was equipped with lateral vector transporters, a design deemed obsolete by the late 2240s. (DIS: "The Vulcan Hello", "Battle at the Binary Stars") The Walker-class brig was located on deck nine. (DIS: "Battle at the Binary Stars")
The Walker-class was named for NASA test pilot Joe Walker. (Star Trek: Discovery The Official Starships Collection, issue 1, p. 10) A photo of Walker standing next to Little Joe, a Bell X-1E, was used as set decoration in the Shipyard Bar, a location visited in the film Star Trek.
The Walker-class, represented by the USS Shenzhou, was designed by John Eaves in conjunction with Star Trek: Discovery production designer Todd Cherniawsky, under guidance from co-creator Bryan Fuller who requested that the ships have a lower profile than that of the original USS Enterprise and possess angular nacelles. In order to rationalize this divergent design ethic, Eaves and Cherniawsky speculated that Starfleet of this era might have deviated from earlier, Vulcan-inspired designs, or that the Shenzhou and Discovery originated from a different production base than the Enterprise. (Star Trek: Discovery The Official Starships Collection, issue 1, pp. 9-10)
The Walker-class was meant to incorporate elements from Enterprise NX-01 from Star Trek: Enterprise and the USS Reliant from Star Trek II: The Wrath of Khan, as well as 1940s aircraft. The distinctive red livery adorning the Shenzhou was added after the design was finalized and the Atzec-patterning deemed too subtle. Eaves also created a rendering of the ship with turquoise livery, but this was not utilized in the final design. (Star Trek: Discovery The Official Starships Collection, issue 1, pp. 10-13) Eaves also produced a four-nacelled concept design for this class of vessel, in mid-July 2016, which later played a part in inspiring the design of the Cardenas-class. (Star Trek: Discovery Designing Starships, p. 74)
According to Eaves, "the only real note I had was that the bridge was going to be on the bottom, plus we knew it was going to be an older ship." During the process of designing the Shenzhou, many of the variety of designs Eaves conceptualized would be later used for other Starfleet ships. In finalizing the design, "I wanted something non-traditional to tie it all together. I thought about something that Tony Moore at Edwards Air Force Base told me about, which was a 'blended body' aircraft, where everything smoothly transitions into itself, so the hull blends into the winds and so forth [….] So my hull blended with the saucer." The final product resulted with "a body that arched across the top of the saucer with the bridge on the bottom, so it had all the necessary elements, but in a new layout." (Star Trek: The Art of John Eaves, pp. 188-191)
According to technical data prepared for the San Diego Comic Con in 2018, the ISS Shenzhou had 13 decks, a crew complement of 150, a maximum warp of 6, and two impulse engines (approximate warp factor 0.3). 
The Walker class issue of the Star Trek: Discovery The Official Starships Collection further claims a length of 423.4 meters. This would make it about 1.5 times as long as a TOS Constitution-class starship (whose size was increased by a factor of 1.5 itself for Star Trek: Discovery).