A simple way of illustrating the three alchemical phases, and how they can unfold within a limited scope and over a short timespan, is The Work.
In the context of The Work, the nigredo is the misery of the situation, prompting us to explore it through the four questions and the turnaround.
The albedo, the purification, is the process of genuine inquiry. We clarify the situation by seeing what is already more true for us than what initially appeared to be true, simply because we held onto a particular belief.
And the rubedo is the release, and what we emerge into, at the end. This includes embracing the polarities of the initial statement (the one we believed in and subsequently brought up stress) and all of its turnarounds, finding the grain of truth in each of them, and so being released from blindly believing any one of them to the exclusion of the others. In this process, there is also a recognition and integration of the shadow (I find in myself what I initially only saw in the others, and in them what I initially only saw in myself.)
The alchemical vessel is the willingness to admit that something is not working, and to sincerely explore it through a process of self-inquiry. And there are other aspects of the vessel, such as the obvious ones of being conscious and well-functioning enough to do the process, and also of having access to (knowing about) the process. Especially in the beginning, a part of a good vessel may also include being facilitated by someone familiar with the process.