The first 45 pax to check in (by any means - on-line or at the desk) receive a boarding pass endorsed with the letter A.
The next 45 to check in get a pass bearing a letter B. Everybody else gets a letter C.
When the aircraft arrives at the gate, it has often come from elsewhere and will continue onwards under the same flight number. Those who wish to deplane, do so. Those who wish to stay on board for onward travel are asked to stay seated in their original seats until a head count has been completed - then they are free to move rows and sit wherever they wish.
When boarding starts, they start with the "pre-boards" (aged and infirm, wheelchair, families with kids (or, more often 7 adults and one kid (never did understand the make up of those "families")). The pre-boards can sit anywhere they wish - except the emergency exit rows.
Then, in open boarding, all the letter A's go first and sit where they wish. Then the B's follow suit - then the C's all board and sit where they can.
That's it -- until the next stop (at which point they hit the replay button and it all happens again).