New homeowner- don't know how HVAC works!
Your heating and air conditioning may be one system or two. A heat pump does both heating and AC. But if you have a furnace, then there will be a separate air conditioning unit. Typically, the heat pump or AC compressor unit is outside the house, sitting on a small concrete slab. It requires little maintenance, and that is normally done by a professional. If you have a furnace, it may be in the basement or a closet.
There are electric and gas furnaces. You could have either one. You can tell if you have gas appliances if you receive a bill from your local gas company every month. Gas appliances might include a furnace, a clothes dryer, and a water heater.
Water heaters are either gas or electric. If gas, it usually resides in a closet or garage, while electric ones are often in basement or crawl space under the house.
In appearance, they are metal, usually white, cylinder-shaped.
You could probably find a friend, co-worker, or neighbor who would walk you through the house, pointing out useful information like this. I'd recommend it (partly because it takes too much typing to go on).