Because many of the new engines run at higher temperatures than power-plants of earlier design, oils have been improved accordingly. Make sure you use only the manufacturer's recommended oil when refilling. The auto-makers recommend SF, SF/CC or SF/CD grade oils for the latest gasoline engines and SF/CC or SF/CD oil for diesels. Some also specify viscosity, usually opting for 5W30 in most climates. Some carmakers may not repair your engine under warranty if the dealer thinks you caused the rings to stick by using the wrong viscosity oil. If your car is under warranty, make sure that your parts store receipt includes grade and viscosity and then save it as part of your maintenance record, noting the mileage and date at which the oil was changed.
For older gas-engine can you can use SF oil even if SE or another grade is specified in your owner's manual. SF is just an improved formulation that stands up better under the rigors of high temperature and contamination.
Once you're certain that you have the right oil for your car, fill the crankcase with the recommended amount, start the engine and run it for a few minutes. While it's running watch closely for leaks from the filter or drain plug. If everything's okay, shut it off and check oil level on the dipstick. If you're certain you used the recommended amount for a change with a new filter but the dipstick shows low or overfilled, stop by your dealer with the dipstick and make sure its the correct one for the engine.
Between changes, make sure you check your oil level at every other gas fillup. And, when it's low, add the same type of oil you used when you changed it last.