Vizard Creation Process

Process 1:
This process is based entirely on force of will by a normal soul, though with the intention of gaining Shinigami powers it doesn't have access to or failing and becoming a Hollow. Becoming a Vizard is an extremely rare occurrence of this process. When Ichigo's spirit chain was completely eroded he underwent the normal transformation of a Plus into a Hollow. The significant difference is that normally, when a Plus transforms into a Hollow, the spirit form shatters and reconstitutes itself into the new, monstrous form; Ichigo's transformation was entirely out of sequence, as the Hollow mask was being formed first while his body was still that of a Plus (showing that he was resisting the transformation). Ichigo enters into an internal world where he is forced to find his spiritual powers in a small amount of time, by sheer coincidence he does so, but in the middle of becoming fully transformed into a Hollow. Therefore, it is that singular moment that allowed Ichigo to gain both Shinigami powers and acquire Hollow powers at the same time.

Process 2:
It is unclear how the other Vizard gained their current status. What is known is that Sōsuke Aizen was instrumental in the Hollowfication process (though whether he knew of the full potential of the results is left to be questioned). This process used seems to spread as some form of possible infection through wounds, that has the desired effects on souls with high-level spiritual energy as compared to souls with low-level spiritual energy, causing those infected great sickness and fatigue, until they vomit up a white liquid that forms the beginnings of their Hollow mask, which then proceeds to transform their bodies and warp their minds. Other than that all that is known is that the process is accelerated by aggressive emotions. The conclusive result makes a Shinigami into a primarily Hollow-like humanoid, which is a highly unstable transformation causing mindlessness and aggression.

Process 3:
Aside from the dangerous method used by Urahara on Ichigo, the Hōgyoku could allow a Shinigami to use Hollow powers (presumably in relation to the Vizard creation), but it has only been shown doing the opposite (creating the Arrancar). Urahara's Hōgyoku played a vital part in the process of making the Vizard currently what they are, as he tried to use it to return them to their previous state. But according to Urahara, what his device did was not what he had intended (turning them into a stable form of complete hybrids) and he considers the solution a failure on his part, though they didn't become complete Hollows due to his intervention and did eventually gain control over their new power.