There are various kinds of qualitative and quantitative data you could collect in an impact evaluation. For example:
It is important that any process evaluation does not change the intervention as a result of trying to record it. For example, observing all intervention classes could change the way teachers teach them. Observations should be unobtrusive, done on only a sample and balanced across the treatment and control groups.
You should carefully select just the data that is most relevant. You should also ensure, particularly when collecting qualitative data, that the person doing so is as independent as possible. Anyone who is committed to and has put effort into making something work may find it hard to report neutrally on it.
Finally, this kind of process evaluation data is a complement to a good impact evaluation data. It should not substitute for it because a process evaluation cannot tell you whether something has worked, only how it has (or hasn't) worked.