Your measurements are for estimating and ordering. On stone or solid surface, a fabricator will template the actual cabinets before cutting, and there is a good reason they insist on it.
Measure each run of countertop separately, wall to wall or wall to the end of the run. Take the length at the back against the wall rather than along the front edge, because the wall is the constraint.
Depth is the cabinet depth plus the overhang. A standard base cabinet is around 24 inches deep and countertops typically overhang the door front by an inch or so, putting most worktops near 25 to 26 inches. Confirm the overhang you want rather than assuming, because it affects both material and how the run feels to work at.
Measure the depth at both ends of a run. If the wall is not straight, or the cabinets are not perfectly aligned, the depth needed varies along the length and the fabricator has to know.
An L-shaped or U-shaped kitchen has runs meeting at corners, and each junction is a decision.
Measure each leg to the corner. Then decide which run passes through and which butts into it, because that determines where the seam falls and which piece is cut square.
Seams matter on stone. They are visible, they are a weak point, and a good fabricator places them where they are least conspicuous and least stressed, which is generally not across a sink or a hob cutout. Flag the sink and hob positions when you send your measurements so the seam plan accounts for them.
Stone comes in slabs of finite size, so a very long run may need a seam whatever anyone prefers. If a seamless run matters to you, ask about slab dimensions before finalising the layout, because the answer may change where you put the island.
Every cutout needs its own measurements and its position along the run.
Sink. The cutout depends on whether the sink is undermount, inset or integrated, and the manufacturer supplies a template dimension. Measure the position from a fixed end, and check where the base cabinet's internal structure sits, because a sink cutout cannot land on a cabinet side panel.
Hob or cooktop. Same again, plus the appliance specification usually states minimum clearances to the front and rear edges and to any adjacent wall.
Tap and accessory holes. Count them and note their positions. These are drilled at fabrication, not on site, on stone.
Measure cutout positions from the same reference end as the run length, so everything sits on one coordinate system rather than a mix of measurements from different corners.
An island needs the overhang measured on every side that has one, and those often differ: a seating overhang might be 12 inches while the others are 1.
A seating overhang beyond a certain projection needs support brackets, which is a structural point rather than a measuring one, but the measurement determines whether you need them. Ask the fabricator for their threshold.
Also measure the clearance around the island to the surrounding runs. It is easy to design an island that fits the floor and leaves an aisle too narrow to open a dishwasher in.
On stone, quartz or solid surface, a professional will template the installed cabinets before cutting, usually with a laser templating system, and they will not work from your numbers.
That is not distrust. It is that these materials cannot be adjusted on site. Wood can be planed and laminate can be trimmed, but a quartz worktop cut a quarter inch short is scrap, and it is expensive scrap. Templating captures the actual as-built geometry including every wall that is not straight.
So your measurements serve a different purpose: getting an accurate quote, choosing material quantity, and checking the layout works before anything is committed. Treat them as the planning number, not the cutting number.
Laminate is the exception, since it is cut on site and adjustable, so careful measurements can go straight to a supplier. The full kitchen method is here, and the backsplash follows once the counter is in.
Still working out which laser measure to buy? The front page narrows it to eight.