What I have seen and read is about traditional monk’s way of study. And I guess the lay people’s way is also not largely differs from this.
Generally monks study Suttas or Vinaya or Abhidhamma starting from the beginning of each,
while using Visudhimagga, Matikatthakatha(or any brief summary book of whole Vinaya) and Abhidhammatthasangaha for reference and guidance, respectively.
Some monks start from Abhidhamma, because some senior monks advise them to start from Abhidhamma to protect the view and cover the fundamentals. (as for venerable Nagasena in Milinda Panha, Analytical monks, Burmese monks, Study monks etc.)
Some monks start from Vinaya.(Because it is the beginning and protection of monk-life )
Some monks start from Nettippakarana or Suttas. (Because they are faith developing and encouraging for practice).
Most of the monks are needed to memorize(at least parts of) Paritta book, Dhammapada, a Samanera advice-book and Pali beforehand. (Because they are considered to be prerequisites)
And some monks study switching between each other Pitakas while keeping the mentioned 3 guidance books as reference.
Nevertheless, apparently, most of the monks have a preference out of the three pitakas (I don’t know whether this is good or not).
Most of the traditional lay people (only if they like studying dhamma), formally start from studying Abhidhamma basics.