Binondo is the "Chinatown" district in Manila. From Ninoy Aquino International Airport NAIA, you can take the cab going to Binondo.
By LRT, take the Baclaran station and dropoff at Carriedo station which is at the edge of the Chinatown district called Santa Cruz. The Santa Cruz arc/shrine is a few walks a way from the LRT.
From this point, you can either walk, take pedicabs/tricycles, calesas (horse-driven carraige), or jeepneys that would take you within Binondo.
If you decide to go on foot, look for the Santa Cruz shrine/arc, it is opposite the Santa Cruz plaza. Walk through the small street within the Santa Cruz Arc and you're already at Ongpin, Binondo's chinatown district.
It's a crowded, very busy place - if you ever feel lost, just ask anybody from any of the jewelry stores lining up the street and they will gladly give you directions.