Tires, you need a tire pressure gauge, they cost about $3. Since the car is new, you should check them weekly, and familiarize yourself with the shape the tire holds when properly inflated. Use the owners manual to tell you what pressure to use. When the tire looks flatter, or more bulgy at the bottom, it’s low, and probably 10psi too low, you’re better off checking regularly and filling it up before it gets that bad. You should also inspect the tires regularly, make sure they are solid, have good tread depth and are not damaged or cracked on the sidewalls. Tread depth should be greater than the distance from the edge of a penny to the top of Lincoln’s head.
Oil, check the owner’s manual for the # of miles and/or time between changes. You can’t go wrong following their recommendation. You should also check the oil regularly, there will be some brightly colored sticks with loops on the end inside the engine. These are dipsticks, used to check the levels of oil, transmission fluid, that sort of stuff. Check your manual for which one is oil. You pull out the stick, wipe it clean, then fully reinsert and remove the stick to check the level. It should be between the two marks on the stick. The same goes for the other dipsticks, whatever they measure.
Under the hood, let’s stick to the basics. At the front is the radiator, where your engine coolant is cooled down by air, so the engine doesn’t overheat, it looks like the back of an air conditioner. Check your manual on how to fill the radiator. Do not ever open up the pressure cap (the metal cap with little wings) when the engine is hot. Always use a proper mix of antifreeze and water in the radiator, not pure water or pure antifreeze, the bottle will give you the recipe. You can use pure water in a pinch, but it will freeze in winter, so you want an antifreeze mix. Check the hoses coming from the top and bottom of the radiator to be sure they are in good condition.
Cooling the radiator is a fan, which is either powered by a motor or a belt attached to the engine. Which brings us to belts. There will be one or more black rubbery looking belts wrapped around pulleys, these power various things in the engine, like your alternator and air conditioning unit. Inspect the belts to be sure they are not cracking, fraying or falling apart. The manual may advise changing them at specific intervals.
There will be a plastic tub filled with blue liquid, that’s your windshield washer reservoir. Make sure it’s full with a proper washer fluid, you can top it off with water in a pinch.
The rubbery wires that attach to the engine are your sparkplug wires, they should be clean and in good condition. You should also have the plugs changed regularly (again… the manual)
There’s probably a big square plastic box with a big channel going to the top of your engine, this is the air intake and the box has a filter in it. This could also be a big round thing on top of the engine. You simply open the compartment and swap out the filter when it’s dirty.