For convenience, I advise you to download and use the Grab app. It's an affordable private car service that can take you from one point to another, similar to Uber. You can use this app to travel from the airport to your intended destination. Metro trains and buses are also available on Metro Manila's National Roads. Finding transportation in this area is relatively easy, however, the main challenge is heavy traffic during rush hour, so it's advisable to plan your trip accordingly. Which city in Metro Manila you are planning to stay in?