Malindo Air, Jet Airways, Malaysia, are the carriers that will take you to Kuala Lumpur airport without a stop. Connecting flights are offered by Singapore Airlines, Jet Airways, Malaysia, Silkair, etc.
The airports that are situated closest to PJ are Sultan Abdul Aziz Shah Airport, Kuala Lumpur International Airport and Batu Berendam Airport. All the three have both international as well as domestic flights coming in daily.
You can choose to rent a car to take you into the city. However, there are also several metered taxis available to take you to PJ.
Take the Kelana Jaya railway line which travels from Kuala Lumpur to central PJ. The main stops are Taman Jaya, Asia Jaya, Taman Paramount and Kelana Jaya. Another option would entail taking the KTM Komuter electric trains and getting off at any of PJ's various stations.
Buses come into Petaling Jaya from Kuala Lumpur, Singapore, Klang, and more. There are metrobuses as well as other more comfortable ones like the Aeroline, which has a double-deck. The main buses from Kuala Lumpur stop at Asia Jaya, Damansara Uptown and Bandar Utama. There are also stopa along the Federal Highway, where you can get on.