Well, I excluded the details of minecarts because I haven't really used them yet, either...
Burrows is 'easy'. For the dedicated block-cutters, set up the workshop(s) and stockpiles (inwards, outwards and supplies) and beds/dining facilities as you wish) and paint over these all with a burrow. (You can paint over the separate areas that these exist[1], but I'm assuming you're putting them in close proximity.) In the workshops, manage them to only allow given dwarves to work in them, and for the burrow set them up as the place those given dwarves wish to be.
While things don't got to hell-in-a-minecart you should find said dwarves only take jobs (and materials) from the burrow (whether that be block-making or eating or sleeping) and while they are free to wander outside the limits (or between, if separated), you should have made it so that they feel no need to wander any further than you'd consider necessary.
@AutomataKittay: Setting up a burrow on dwarves actually doing a 'area forbidden' job (where they're fetching from outside the burrow limits, especially, or have flagged such in their 'job queue') probably tends to create your cancellations. To this end I'd usually get them assigned to cutting blocks (having nulled all other masonic jobs for the duration, maybe) and then assign them to the burrow while they're well within it and doing the block-making/whatever. Re-assign these extraneous jobs once it's sorted. When looking for new jobs they should find totally in-burrow bits of stone (or in-burrow supplies to eat and drink of, or in-burrow beds to sleep in, although if they don't they'll 'suffer' a bit longer and only wander out when they're
really fed up of the 'confined' situation.) When adding further dwarves to the confined jobs, just pick your moment. (Helps if the meeting area or dining room is within your space and you choose one who is already in there doing whatever... Once they've finished, they'll look for an in-burrow job, find one and start it, no fuss.)
Or at least that's how it tends to work for me. I use civilian burrows
extensively[2], and yet military-alert/refugee burrows
never, making sure that peacetime burrow designations (and, for the unburrowed, their default work areas that they want to wander round) are already within the confines of the 'safe' area. Playing styles vary, of course and this might not work for everyone.
[1] Or even eventually assign each dwarf separately to each and every one of the "workshop" burrows, "stockpile" burrows, etc, that you need, but you might as well keep it simple with one.
[2] My favourite use, actually, is to define (for example) a cavern-exploration shaft or two (stairway(s) to find caverns) as an Exploring burrow, assigning one miner exclusively to that (give or take a supplies/sleeping area), while defining the
simultaneously sought after underground field area (or other current needed excavation area) as a PriorityDigging burrow and assign another miner exclusively to
that (ditto with attached supplies/sleeping area). This way I don't get the room dug out but no exploring or the exploring being done but none of the other priority stuff going on, without otherwise re-jigging the mining jobs to ensure that only one miner
can work at the (naturally chosen) 'priority' mineface and the other taking the next (naturally chosen) priority area. And I can also map out entire complexes of rooms and only 'open them up' to being mined as I want to, without having to unpaint digging designations at the edge of the currently opened areas and then re-paint them (and remove further bits at the next 'firebreak' between jobs) to stop them being dealt with prematurely. Easier to do than to describe, though!