What did Noah's ark look like?

Short answer: we don't know. Genesis gives the raw dimensions, but says little if anything about the shape. Terrence Mitchell says that:

While [6:16] can be taken in the traditional sense of describing three stories, it is also possible to understand it to indicate three layers of logs laid crosswise, a view which would accord well with a construction of wood, reeds and bitumen. The Illustrated Bible Dictionary, 1:110.

Here's one hypothetical design, which shows how different it might have been than popular representations:

Meir Ben-Uri Rhomboidal Design.

Reported by Ya'Acov Friedler "What the Ark was Really Like" Jerusalem Post 10 Oct 1967 

Friedler, a reporter for a major Israeli newspaper, describes Noah's Ark as proposed by Mr. Meir Ben-Uri. His ark is 150m (492 ft) long, weighed about 6,000 tons and had a carrying capacity of 15,000 tons. Ben-Uri, Director of the Studio for Synagogual Arts took several years to complete his study, based on the numerical values of the Hebrew words of Genesis 6:14-16. From this he prepared a scale on which he based his measurements, which led to a cubit length of 500mm (19.7 inches).

    

Image The Jerusalem Post 1967

The most striking aspect of Ben-Uri's ark is the rhomboid cross-section - almost a Vogt hull in appearance, but with a "V" bottom (deadrise). Ben-Uri claims a rectangular vessel would have less space inside due to the need for a "maze of supporting beams", and that the rhomboid design is more buoyant. (This is testable, the enclosed rhomboid has exactly half the area of the bounding rectangle, so the interior space is halved. Worse, the sloping sides will make inefficient use of space. There is also no reason to expect the rhomboid will have substantially less interior structure than the rectangular hull. TL)

The roll stability of Ben-Uri's ark is a substantial improvement over the Vogt hull, but it is not as stable as the rectangular hull.  The rhomboid design is also very sensitive to variations in draft.

Naval architect Dr Dan Khoushy commented on the design; "I would not have chosen this shape for the vessel, but I must say that it is practically optimal for the purpose;

According to Ben-Uri, the hull would be built up in identical triangular compartments, forming ten "holds" in a virtual "mass production" process. Laying the ark on one side, the roof mounted door would be accessible, but when buoyed by the floodwaters the door is in the roof. (Seems like a lot of effort walking around on sloping floors for the sake of sealing a little door. TL)

The last claims of the article refer to the cubit length being the same as for Solomon's temple, which is an interesting point, and finally that the reed basket of baby Moses may have been rhomboid also.  (This assumes "tebah" refers to shape, and make the dubious assumption that Jocabed took a rhomboid basket when Egyptian reed basket were more likely rounded.

http://worldwideflood.org/general/ark_history.htm