Tires
You should check the pressure in your tires weekly. If your tires are over or under inflated, it causes your gas mileage to go up. It can also cause other damage to your car if you let it go long term. You should always check the tread on your tires. If your tread is below 2/32", your tires are bald and you need to replace them. There are many different sizes of tires. You can check inside the door and your tire size is usually on a label.
Oil
Most cars nowadays let you know your oil life. You should change your oil every 3000 miles. Use the proper oil for your car's engine. Keeping the oil changed regularly will help your engine last longer. Always check if you see an oil leak and get that fixed right away. You need clean oil and the right oil to maintain your car's longevity. When your oil is changed, your oil filter should always be changed. An oil change is relatively inexpensive, especially compared to the issues you can have with not properly taking car of the oil in your car.
Other fluids
Brake fluid and transmission fluid should be checked regularly and topped off when necessary. If you see that they continuously need fluids added, you need to see a mechanic.
Cabin Air Filter
The cabin air filter should be changed regularly. It should be changed at least once a year and most people do it more often.