How does kamma create a new set of aggregates for a rebirth; how do the mechanics of this process work? In the booklet "A Discourse on the Bhāra Sutta", by The Venerable Mahāsi Sayādaw, I read the following:

"As we make great efforts to fulfil desire, kamma and mental formations are brought into play. They create new aggregates. So, after one life we go over to another in a new groups of five aggregates, by virtue of the craving prompted by delusion. As a result, we are left with the burden of aggregates to carry." Please refer to Part II (Table of Contents), Threefold Craving (Section), Sensual Craving (Subsection)

Is this process to be learned or understood during the course of vipassana meditation, or taken on faith in the course of instruction?
The workings of kamma is actually one of The Four Imponderables (acinteyya), i.e. questions that the Buddha deliberately did not answer. These questions can only be understood by a fully enlightened Buddha. If one is not a fully enlightened Buddha then thinking about these questions will only leave the mind distressed and agitated, i.e. unfit for meditational practice.

By doing insight meditation one can verify for oneself that phenomena can spawn new phenomena thereby leading to further becomming. This also occurs at the break up of the physical body. The defilements do not "die". Only the physical body breaks up but the defilements find a new body to arise in. 

Don't take my word for it or any other persons word. Not even the Buddha's word. He taught that we should not blindly believe what he said but instead go and test these things for ourselves through experimentation on reality, i.e. by doing insight meditation.

Hope this helps. If you have any questions to what i wrote let me know.