I get your situation completely, and every part of the pool system was mysterious at first. I embarked on a mission to map the entire pool system, and this has proved invaluable especially during the winter storm.
To start with, I suggest that you: (i) identify the pump's brand name and model number, look up its manual online, and note down how to drain it (usually you have to unscrew a small roughly 1-inch plug at the base of the pump); and (ii) identify the water filter's brand and model, and locate its drain plug (naturally, you should expect it to be close to the base of the filter).
Do remember to keep a decent flashlight, basic tools, gloves, etc. handy in case this stuff has to be done at night!
There are more expert members on this forum who can shine more light on this topic. In the interim, here is the link to a YouTube description of crisis-mode equipment draining:
In the future, I am leaning towards pre-emptively draining my equipment before the big freeze, instead of the last-minute brinkmanship.
Finally, I wish the equipment manufacturers start listening to non-expert users like us, and redesign the systems to make the key parts like drain plugs easier to find. To start with, put a sticker with EMERGENCY instructions, label the drain plugs, make them all similar in size and shape so one does not need multiple tools to operate them, and manufacture the plugs in brightly colored plastic instead of black. Make the knobs big and easy to locate. How about bright yellow

.
Perhaps, they could make all of the draining happen at the press of a button
The possibilities for progress are endless.