Buses to Malabar operate along Anzac Parade from the city. For buses to Malabar Beach, the 399 bus runs to and terminates there. All other buses (393, 394, L94) stop right in the heart of the Malabar shopping area on Anzac Parade.
There are no train stations near Malabar but you can get off at Central Station to connect with the 393 bus. You should be able to find your way to Central from nearly everywhere on the CityRail network.
Malabar is a 14km drive south-east of Sydney city. It is a very quiet beachside suburb so there are no parking meters or difficulty in finding a parking space to worry about.