Best way to get to the city from Manila International Airport
Manila Ninoy Aquino International Airport (commonly written as NAIA) is only 10km from the city center and 5km from Makati, yet it's not very well connected to the city
The best way to get to the city from the airport as of 2019 is by taxi. You can also take public transportation option, but it's much slower and only recommended if you have light luggage
How to take a taxi from Manila airport to the city:
Taxis take 10-20 minutes to get to Makati and 30-45 minutes to get to downtown with normal traffic conditions. Rush hour is between 5:30pm and 7pm, and during this time the travel time can 2X
There are 4 kinds of taxi serving the airport: yellow taxi, Grab, coupon (fixed rate) taxi, white (street) taxi
Yellow taxis (best option for most visitors): It's the official airport taxi and it's metered. Highly regulated and very safe. Downside is that the queue tends to be very long, 30 minutes to 1 hour wait is not unheard of. Fare to Makati ranges from 200-300 PHP ($4-6USD). Fare to downtown is 300-450PHP ($6-9USD). Simply exit the terminal building and look for these physically yellow taxis. You will find a sign that says "Yellow Metered Taxi Entrance" at the start of the queue
Grab (my personal favorite option): works like Uber, very popular here in Manila and other Southeast Asian countries like Thailand, Malaysia and Singapore. I use Grab almost exclusively when getting around Manila. The price is fixed by the app so you have little risk of getting scammed. You can use their fare estimate page to get a sense of how much it's going to cost you to get to your hotel. Put in "Ninoy Aquino International Airport" as your origin. Obviously you need to have the app downloaded and set up on your phone to use it. The app will tell you which door to meet your driver.
Coupon taxi (safe and reliable but expensive): Also an official airport taxi, but they are much more expensive than the yellow taxis. Unlike the yellow taxis, their fare is fixed by zone, and you purchase the coupon ahead of time instead of paying a metered fare. Fare to Makati is 440PHP ($8.5 USD), and fare to downtown is 600PHP ($12 USD). They are white in color, but don't confuse them with the white street taxis. The only place to buy tickets for coupon taxi is inside the terminal building at one of the dispatcher desks where you tell the which hotel you're going to and they tell you which zone it's in and how much your fare is; you cannot buy coupons outside or in the car!
White taxi (street taxi I don't recommend for first time visitors): they're cheap but not cheaper than Grab. With Grab being so readily available, there's very little reason to take these taxis. They are the normal Manila street taxis and since a few years ago they've been allowed to take passengers from the airport. They are not as regulated as the other taxi options, so there's a higher chance of getting scammed. If you take these taxis, insist on using the meter, and track your movement on GPS to make sure they're not taking a long route. If you want to use them, I suggest using Grab's fare estimate page to get an understanding of how much the fare should be beforehand. Fare to Makati is around 150-180PHP ($3-3.5 USD), and fare to downtown should be around 170-220PHP ($3.5-4.5USD). You find these taxis outside the terminal building, behind the yellow taxis
Ignore any touts who come up to you inside the terminal; there will be many of them and they can be very persistent. They will usually massively inflate the fare. I've heard some tourists getting quoted over 1200 PHP ($23USD) to go to Makati, which is ridiculous and should never be paid.
How to take public transportation from Manila airport to the city:
Airport bus:
UBE Express is the bus service launched a few years ago that connects various area of the city with the airport
It's a very comfortable airport bus that can take you to downtown and Makati. It has 4 routes, the details of which can be found here
Fare is 100PHP ($2 USD), so it's very affordable. It's available at all terminals
It runs 24 hours a day from terminal 3, and between 8am and 10pm terminals 1 and 2
You can buy tickets inside the terminal at dedicated counters. Look for signs for "Premium Airport Bus"
My take on this bus is that it's not really worth the hassle. 100 PHP bus fare is cheaper than taxi, but it's only a few USD in difference. For this few extra USDs, a taxi is much more convenient by dropping you off right in front of your hotel. Also, if you check its page on Tripadvisor, it has a terrible record of being on time and customer service.
Overall I don't recommend it
Bus + trains:
This is the cheapest method by far, and the entire journey will cost you around $1 USD. However, it's very cumbersome as you need do transfers in very crowded stations. I only recommend it if you have 1 piece of light luggage
If you're at terminal 3, you can find bus Route 2 outside the terminal building that can take you to EDSA LRT / Taft MRT station (both stations are located together and connected to each other), which are both very close to the airport. Fare is 20PHP (40 cents USD)
At EDSA LRT / Taft MRT station, transfer to the train. If you're going downtown, you need to take the LRT train from EDSA LRT station. If you're going towards Ortigas and Makati, you need to take the MRT train from Taft MRT station. Fare is going to be 20-30 PHP (40-60 cents USD)
Here's a link to the LRT/MRT system map. There is only 3 lines so it's very easy to understanding (LRT is line 1/green line. MRT is line 3/yellow line on this map). EDSA/Taft stations are at the very bottom of the map