Reading the number
Below −0.3 the water is under-saturated and dissolves calcium from wherever it can find it: plaster, grout, heater cores. Above +0.3 it is over-saturated and drops calcium as scale on tile, in the salt cell and inside the heater. Both are slow, expensive damage. Zero is the goal, and anything inside ±0.3 is fine.
Which lever to pull
pH moves the index fastest and is the cheapest to adjust, so start there. Then alkalinity. Calcium is the slow, structural one: get it into range once with the calcium hardness calculator and it stays for the season. Temperature you can't control, which is why a pool that was balanced in May reads scaling in August.
Why CYA is in there
A test kit's alkalinity reading includes cyanuric acid, which doesn't buffer the way carbonate does. The calculator subtracts a third of your CYA to get carbonate alkalinity, the number the index actually depends on. Skipping this correction is why many online LSI tools read high on stabilized pools.