Well, I must admit that I've gotten lazy over the years amd tend not to test water parameters nearly as often as I probably should. Regularily I test salinity during water changes and if I have to make a larger top-up then normal, and TDS on the water that I'm making for the water changes.
I tend not to test anything else unless I notice something doesn't look right, like corals not opening (when I had them) or fish missing for a couple days etc. The only time I do regular testing is when I get a new batch of salt and test for everything for the first couple water changes just to see if there is any adverse reactions or if I have to change my Kalk drip rate because the salt batch wasn't the same as the previous ones.
I also test the water about a week before I get any new live stock and weekly for about a month after adding something new to the tank just to see how the new livestock affects water parameters and to see if I need to change my maintenance in any way.
I have all the test kits at hand but like I said, I've gotten lazy over the years and rely mostly on my livestock and regular maintenance. I would never recommend this sort of approach to anyone just entering the hobby. When I started I tested for everything all the time and took notes on how things changed over time, how my animals reacted differently when things went wrong and paid close attention to how all the chemicals, water changes, live stock additions and everything else interacts together visually as well as watching the test results. If I suspect something is off, all the test kits come out immediately.