How do these lizards actually accomplish bipedal locomotion?

In 1949, Richard Snyder set out to determine how lizards execute bipedal motion. To this end, he took high speed videos (64 frames per second) of Basiliscus basiliscus exhibiting the behavior and analyzed the movement from three different perspectives. Snyder was able to conclude that the forelimbs do not play an important role in elevating the anterior section of the torso, but that the epaxial muscle in the back allows for this maneuver. Snyder observed that Basiliscus can begin bipedal motion from a resting position with a thrust by both hindlimbs of the animal followed by one hindlimb rapidly swinging around in a lateral arc to catch and support the weight of the body and take the first bipedal step. It has also been observed that Basiliscus can commence bipedal motion from quadrupedal motion by raising the anterior portion of the torso and head. Snyder presents the diagram shown below of the physical stages of bipedal motion. Snyder notes that the proximal portion of the elongated tail of Basiliscus is elevated during bipedal motion, although the tip of the tail may drag. He also determines that the tail acts as a counterbalance to the trunk and head of the body. Snyder tested his theory by removing portions of the tail of a Basiliscus, allowing it to acclimate, and inducing bipedalism. As the length of the tail is shortened, the ability of the lizard to execute bipedal locomotion is negatively effected. Sufficiently shortening the tail can prevent a lizard from being able to move bipedally.

Joshua Laerm performed another experiment using Basiliscus basiliscus in 1973. In this experiment, Laerm set out to determine any differences in bipedal mechanics on different substrates. High-speed motion pictures were taken (300 frames per second) of lizard bipedalism in water and on a sandpaper-covered platform. From these recordings, he was able to determine that there is no difference in the basic motion of bipedalism based on substrate. There are, however, observable differences in terrestrial and aquatic bipedalism. He explains that the lateral undulation of the spine is exaggerated in the aquatic form of this motion. The reason for this, they explain, is to counter drag in the water. There is also a difference in angle of trunk incline from a range of 25-35 in water to 20-46 degrees on land.

Laerm also described a special scale on the Basilisk's toe that helps it run across water. The image at left, taken from Laerm's 1973 publication, shows a cross section drawing of the second phalange of the third toe in an iguana (A) and a basilisk (B). This special scale is visible here as a fringe protruding from the ventral lateral side of the toe. The image below shows how this structure functions on terrestrial substrate (B) and on water (C). By flaring or compressing this fringe, the lizard is able to travel adeptly over land and water. When the fringe is removed, more of the lizard's body is below the water line, but aquatic bipedal motion is still possible. From this, Laerm is able to conclude that the fringe aids in vertical support of the lizard in the water and in locomotive efficiency, but is not necessary.