Without knowing the specifics of your pool, it is hard to say what exactly needs to be done.
Is your filter hard plumbed or hoses. if it has hoses, you can take the hoses off, and not worry about anything. If it is hard plumbed, then you need to take care of the plumbing - antifreeze may or may not be necessary.
As others said, freezing water expands, and will crack things if is contained. Your skimmer box is one of those things. You can drain your pool below the skimmer, or put a plate or plug on the skimmer entrance, or you can use a gizmo in the skimmer box itself. The first two keep water out of the skimmer, the last gives it something to expand against.
As far as chemicals IN the pool water - bleach, lots of bleach. That's about it. Run it up to SLAM levels before closing, and you should be good.
To give you an idea, for my pool, this is what I do.
I put a plate on the skimmer to keep water out.
I remove the light from my return and replace it with a rubber plug.
I remove my filter and store it in the shed.
I have hard plumbed lines, I leave the valves in them open. This way, any rain water that gets into the skimmer will drain out, and if the plug comes out the return, the pool will drain. My lines have no low spots, it's all downhill from the pool to the filter, so they are self draining.
I run the pool up to SLAM levels and call it a day.
I do take my filter and do end of season maintenance on it. I take it apart, clean it out, replace anything that needs replacing, lube anything that needs lubing, and reassemble. But that's just me. I know people that just open the backwash port, let it drain, cover it with a tarp and call it a day. I like to think mine will last longer, but sometimes people get lucky.
-dave