The knowledge of arising and passing away (udaya-vyaya nana) is arrived at (if the visuddhimagga is to be believed- and I dont see any reason why not to, in line with Mahasi sayadaw teachings) after passing the insight knowledges of nama-rupa, causality, seeing the three characteristics (anicca, dukkha, anatt) and passing revulsion (nibbida- fear of dissolution etc). Then begins the immature stage of arising and passing away. This is then superseded by vipassana upakilesa (which sounds to me like developments of samadhi, in line with the path), which in turn gives rise to mature knowledge of arising and passing away. Even though these are called 'knowledges' or insights, they may better be termed experiences, as they are stages of experiencing the same meditation object which was present at the start- but in different (more advanced) states of mind.
Revulsion, dispassion and cessation (Nibbida, viraga, nirodha ) are the commonly used terms (especially the latter two) in the suttas to denote these stages. Quick arising of stimuli from the sense based are experienced, along with a sense of not reacting to any happy or sad events in the environment. Equanmity of formations (sankhara upekkha) is another term used for the mature knowledge of arising and passing away. Cessation (nirodha) is a stage where the endings of stimuli are seen more and sometimes people get a deep sense of emptiness of themselves (bits of the body actually feels missing). This then flows into release (of stream entry).
It is best to follow a meditation method like that of Mahasi sayadaw to reach these stages- in that system it is well documented how these are reached. (or Pa Uk for that matter I suppose). As far as I know Ajhan Brahm, Goenka, Bhanthe Gunarathana dont speak of these stages of insight much.
The Buddha recommended reaching the knowledge of arising and passing away for lay people here:http://www.accesstoinsight.org/tipitaka ... .than.html