The danger you face when draining a pool too much is that a couple nasty things could happen. The water, which is heavy, and fills up the cavity of the pool, applies pressure to the walls. Too little pressure and the dirt or whatever is outside the pool, pushing back, could cause a cave in. Physics, for every action...
Secondly, too little water in pool could cause your pool liner to become the hull of a boat, and float. The weight of the water is keeping that from happening, like a sunken ship.
They are wanting the water table information to determine a safe distance to drain.
However, if you're not sure, and can't find out, and willing to take on a little risk, you'd probably want to do a few smaller drains of your pool vs. one massive drain. Using the poolmath tab at the top of the page you can put in your pool info and calculate how much CYA you need to drain, which is probably 50% of your pool or more. Adding water back to the top, however, will dilute what's left, and you'll need more than 2x1/4 drains to equal 1/2 of the pool drained. Poolmath is your help there.
To be safe, most guys will tell you if it's an in ground plaster pool to not drain further than the bottom step on the shallow end. So the last step is still submerged slightly. For my pool, and your mileage will certainly vary, that was about a 40% drain.