First thing I will have to learn is what P,S,A, and M means. I assume that "A" means automatic and "M" means manual.
You are 10% of the way there
. P means program mode which is a form of automatic exposure. S is for Shutter priority which means you set how fast the image is capture and the camera sets the aperture (amount of light arriving at the sensor). A is the opposite and lets you set the aperture and the camera picks the shutter speed for you. M does mean manual where you are in charge of both.
I have to disagree with Jack
and say that the best possible mode is "A" for aperture priority. The reason is that the look of an image changes depending on the setting for the aperture. Lower numbers mean less depth of field and higher numbers mean higher depth of field (more things in focus). When shooting a portrait for example, you want to set the aperture pretty low as to have the person stand out. Here is rather extreme version of that where I wanted just the lips in focus:
Here is a more "normal" use of it:
She is standing in a busy street corner yet you can't see any of that. Seems like a studio portrait.
Exact same thing works with animals:
Here is the opposite shot where you want everything in focus:
So for any image you need to decide the look using the aperture. Have the camera pick this and you are going to get random results. BTW, what you see in the viewfinder is with the aperture at its brightest/lowest value. Anything else will have a different look. With experience you can guess what that looks like. Your camera may also have a depth of field preview which can show this, albeit with much darker viewfinder.
Put the camera in A mode and shoot pictures of everything around you. You can start by shooting the keyboard on your computer. See if you can isolate one key vs many. Learn this and just 2-3 other rules and you can put out amazing pictures.
Have fun with your new camera!