NAIA has free wifi in all the terminals (well at least terminals 1-3, not sure about terminal 4 which I've never used in recent years)
To connect to it, just look for any wifi networks with names including "Globe" or "Smart", plus "free". "Smart" networks are usually much faster than "Globe" networks, so go with those if possible
The network speed varies by time of day. If you go early in the morning when there are few other passengers, you can get as fast as 20Mbps download speed, enough to torrent movies. During peak times the speed can get as low as <2Mbps, fast enough for email and Facebook, and maybe YouTube.
If I recall correctly, you will need to enter your phone number to use these networks, and they're limited to 2-4 hours