I have a nice comptometer here… It’s a British one, so the “units” go up to 11 - designed for pre decimal pounds, shillings (20 to the pound) and pence (12 to the shilling).
The principle is simple and in skilled hands can be faster than an electronic calculator - at least a modern electronics calculator. Mostly because you enter all digits in a number at once. So to enter 123, you push 1 in column 3, 2 in column 2 and 3 in column 1 (the right most one) at the same time. So one push enters 3 digits.
Adding is simple repetitive entering and multiplying by the shift and add method.
Girls (for that was who were trained to us them back in their day) could go on training courses - sometimes weeks or months to learn how to use them. They would learn tricks - so e.g. to enter a 9 - well if the other numbers are less than about 5, 9 is 4 + 5, so push 4 then 5 in the same column - this can be faster than moving your hand northwards to enter the 9…
Subtraction is by adding 9’s compliment numbers, and pushing the carry-block key (little silver ones just above the number display near the bottom). Note that the keys have both the positive and 9’s compliment numbers (smaller) on them.
Clear - the lever - and this does 2 things as well as clearing - one is to move the digits in the display down by about a 3rd a rotation and the 2nd is to set a latch to ring a bell on the very next key push. This provides a visual and audible indication that you’re starting with a cleared calculator.
They are very simple in their operation, but can be very efficient in the hands of a trained operator.
I’d get some photos of mine (more or less identical to that, but with the pre-decimal key columns) but it’s under a load of other stuff, sort of packed in preparation for a house move…