[ZenGum]

These "key tasks" are important. You can do a lot toward them without getting your hands dirty.

Tires:
Low tire pressure can cause uneven tire wear and thus shorten the life of the tires and waste money.
It can make the steering seem heavy, and cause the car to drift to one side or the other.
It can (allegedly) cause blowouts.
I can vouch for the first two myself.

You can spot a badly underinflated tire pretty easily. They bulge at the bottom. If one of your tires is a different shape to the others, check it or get it checked.

Oil:
Low oil can ruin your engine. This will be very very expensive. I can vouch for this. (I told you all that I used to be young and stupid!)

Almost all modern cars have a "low oil" warning light somewhere in the dash. This will glow when you first start the car for a couple of seconds, until the oil begins to circulate. Watch this gauge and get used to how long it takes to turn off. If this interval seems to have got longer, you could be low on oil. Check it or get it checked.

Listen to your car as you drive. Once you get used to it, you will notice any new sounds or changes in sounds. But don't go straight to a mechanic and imitate the sound (easy prey). Some guy you know could probably tell you what it is. I have no training as a mechanic but I can tell the different sounds from timing chains, wheel bearings, engine bearings (bad, bad sign) and loose exhaust manifolds.

You spend a lot of money on a car. Take care of it.