When I arrive at NAIA (Terminal 3), where or what door exactly do I enter to have my baggage checked?

The Departure area in NAIA 3 is on the second floor. Before entering the premises you will be subject to xray checks at the door. After that you should proceed to your airline's check-in counter. This is how NAIA 3's check-in area looks like. To know which counter to go to, just ask any ground personnel, or read the screens and check which one's assigned for your destination.
You will be asked to present a copy of your ticket (if you booked online, a screenshot will do) along with your valid IDs. Then they'll ask you to present your check-in baggage so they can weigh it. If you don't have to pay for excess baggage, you're good to go. At your destination airport, there will be assigned carousels where you will be picking up your bags. You will be informed of this by your airline's cabin crew or at the airport. Don't worry, there are plenty of instructions and airport personnel to make things easier.