How to maintenance a car? General maintenance for cars

If a belt squeals after starting the engine or while driving then this indicates a problem with belt tension. Most modern vehicles have automatic belt tensioners which keep the belt at the appropriate tension. Checking the belt tension varies by make and model. Modern vehicles only have one belt, but older vehicles have an individual belt for each accessory of the engine (i.e. power steering, air conditioning, and alternator). Consult a workshop manual for the proper methods for checking belt tension. (The workshop manual or service manual is different from the owner's manual and may be found at the local public library or ordered online). Belts can also be checked by visual inspection and touch for signs of cracking, fraying, or glazing. Glazing means the drive surface of the belt will be shiny.
Hoses can be checked visually and by touch for signs of cracking, swelling, or leaks. If the engine is cool, then squeeze the hose to check for softness. If there is any variation from hose to hose within the same vehicle then that could indicate a problem.
A cooling system pressure tester can be a useful tool to pressurize the cooling system and check for leaks or swollen hoses. This tool be rented from an auto parts store and should come with instructions for use. You'll attach it in place of the radiator cap and hand-pump it as you watch the gauge. Never exceed the indicated pressure that is written on the top of the radiator cap. Most modern cars have a limit of 16 psi. Again, do not open the radiator cap if the engine is still hot.

Vehicle lighting includes instrument panel lighting, warning indicator lights, left and right turn signals, brake lights, hazard lights (which have a distinct circuit from the turn signals even though the display is in the same place), headlights and tail lights, front marker lights, the license plate light, and lights for the cab and trunk. Checking vehicle lighting goes quicker and smoother with two people, and in the case of the brake lights two people are required.
The instrument lighting is all of the backlighting for the instrument cluster (all the gauges, speedometer, fuel gauge and others). The instrument lighting can be checked by turning on the headlights at night or in a dim garage. Check to see that all the gauges are clearly visible. There should not be any dark spots on the cluster.
The warning indicator lights on the dashboard include the brake light, oil light, check engine light, anti-lock brake (ABS) light, airbag light, tire pressure monitor, engine temperature light, and others -- all of which can be found in the owner's manual. All of the warning indicator lights will turn on for a set amount of time (about a minute, but varies per vehicle) when you turn the key to the on position without cranking the engine. Once the engine is running, none of these lights should be on (even the seat belt light should be off, indicating that you're wearing your seat belt). If one is on, then it indicates a problem with its correlating system. The number of lights and types of lights will vary by make and model. Some vehicles have features that others don't, such as traction control.
Exterior lighting is checked with the key turned to the on position in the ignition (or with the engine running, but it's not necessary to have the engine running just to check the lights). Turn on the headlights. Check all four corners of the vehicle. On both sides (right and left, or driver side and passenger side) the same number of bulbs should be illuminated. There should be two front marker lights that are orange, two tail lights, and a license plate light.
Turn the left turn signal on. Check the left front and left rear of the vehicle for blinking lights. Some vehicles have more than one bulb for the turn signal and some even include a signal in the side rearview mirrors. Be sure every applicable bulb is illuminating. Some vehicles have a cornering lamp, which is a clear lamp on the front of the vehicle which illuminates corners while turning. This should be illuminated but it will not blink.
Turn the right turn signal on. Check the right front and right rear of the vehicle for blinking lights. Be sure all applicable bulbs are illuminating. Check the cornering lamp if applicable.
When the turn signal is on and the indicator is blinking fast or not blinking at all, these are indicators of a failed bulb.
Brake lights require two people for inspection. One person presses the brake pedal while the other person checks the rear of the vehicle to make sure all the brake lights are illuminating, including the high mount brake light in the rear window if the vehicle is equipped with one.
Activate the hazard switch. Check to make sure that there are flashing lights with an equal number of bulbs on all four corners. The hazard lights are wired separately from the turn signals, so it is important to check the hazard lights even if the turn signals have been checked.

Consult the owner's manual for the location of the air filter. Remove the air filter. Inspect for visual signs of dirt and debris. Hold the filter up to a fluorescent light; you should be able to see light coming through the filter. If there is any doubt then change it. It's cheap preventative maintenance and it helps preserve fuel economy.