You could but you need to build all sorts of hidden supports underneath.
In theory a thick polycarbonate (perspex/plexiglass/lexan) sheet could easily support the weight but you would have a job anchoring it so it couldn't tip over or tilt and flood. And there would be a big risk if somebody managed to slide under it and get trapped.
In my experience, most horror stories of pool maintenance are usually the result of neglect, or not paying attention to the instructions. It's not that hard, but expect to spend an average of 10-15min per day checking on your pool, adding chlorine, clearing out leaves in the skimmer, etc. Also, once a week, expect to spend some extra time brushing/vacuuming the pool and cleaning the filter.
As a first time pool owner, the simplest thing you can do is pick up a free pamphlet on pool care. Follow the instructions in the pamphlet, and make sure you stay on top of it. My Wal-Mart usually has pamphlets by HTH Pools next to their chemicals.
Start by getting a test strip kit. You dip the strip in the water and compare the colored pads against a chart. Pretty easy (unless you get into a fight with your wife about the shade of orange of the pH pad).
Make sure you pick a good test kit, which measures several properties of the water (should measure pH, stabilizer/CYA, alkalinity, hardness, chlorine). Cheaper ones will only measure a few properties.
Measure your pool every day or so. If the levels are off, adjust them by adding the appropriate chemicals. Just follow the instructions on the container. Most any chemical you need can be found at your local pool store, or Wal-Mart. Beyond that, I'm not going to repeat what you would find in the pamphlet. (Did you get one yet?)
One bit of advice that wasn't in a pamphlet: If you buy "stabilized" chlorine products, they will raise the level of stabilizer/CYA in the pool. If your CYA levels are already high enough, the stabilized product can push your levels over the top. If you aren't sure if the product is stabilized, look for the words Dichlor or Trichlor in the ingredients. Un-stabilized chlorine is usually Calcium Hypochlorite or Sodium Hypochlorite.
Beyond the chemicals, there will be some "mechanical" maintenance/care:
Dirt, pollen, and algae will naturally collect in all the crevices of your pool, so use a pool brush to break it up. Regular churning of the water (from brushing or swimming) will give the filter an opportunity to suck up the debris before it settles.
You will need a vacuum (manual or automatic) to suck up non-floating debris. 48 hours before vacuuming, shock the pool to make sure any algae is dead. 24 hours before vacuuming, add some clarifier to make the algae and dirt settle on the bottom (where the vac will get it).
Make sure your filter is clean. There should be a pressure gauge on the filter that will indicate when too much crud has built up in it (pressure levels will go up). At that point, you need to clean it. Some filters are cleaned by backwashing. Others have a cartridge that needs to be changed. The filter should come with some instructions on how to care for it.
Check the strainer baskets in your skimmer and pool pump. Larger debris like leaves and large bugs will collect there. Periodically shut off your pump and scoop the crap out.
A plugged filter or strainer basket will strain your pump, and maybe cause a burst hose (very bad). So, keep the water path clear.
If you have cold winters, make sure you follow the instructions on winterizing the equipment. I disconnect my pump and bring it indoors every year.
Best Answer
Be very careful about how you deal with this. Decommissioning a pool is not a simple job, and removing an in-ground pool usually requires an engineer to sign off on the plan and you end up with a very big headache if you try to pull off a DIY hack job.
You should also not leave the pool empty. Frost in the winter, and the water table otherwise, produce buoyancy forces that can cause the pool to lift out of the ground and make an even bigger mess for you to deal with. A pool is meant to be underwater and its surfaces, finish, and structure will continue to deteriorate if it is not maintained and operated. The costs to fix it will just get bigger. If you're going to cover it, you need to either keep water in it and maintain it or you need to permanently decommission the pool and fill it or remove it.
A complete removal is the most expensive option, but if you do a complete removal properly, with an engineered plan, you gain two things :
The alternative is to simply fill the pool. This requires at least breaking up or drilling the bottom of the pool to allow drainage and filling it with backfill material. Even in this case you will likely require a permit from your city to do this work. A pool filled in such a manner must be disclosed when selling the house and it will negatively affect the value of the house. If you bury a pool improperly and hide that information when selling you open yourself up to rather unpleasant liability (even for yourself if you don't sell and the rotting, badly buried pool causes erosion that, say, threatens the foundation of your home - your insurers will not forgive your errors). In any case, there will be local regulations that you must follow when filling the pool so be certain that you understand your responsibilities before starting.
The best option here is to consult professionals.