From your origin, ride a jeep or taxi or a tricycle if available to the nearest LRT or MRT station. LRT-2 Santolan Station is near to you if you're coming from Marikina or Antipolo. If you knew your location then it would be very easy to get to LRT or MRT. There are stations of LRT-1, LRT-2 and MRT-3 in almost all locations of Metro Manila.

From Makati/ Pasig/Mandaluyong/Quezon City

Take the MRT to Taft terminal station.
Take the LRT1 to United Nations (UN) station.

From Manila/Pasay
Route: LRT1/LRT2

Take the LRT1/LRT2 to United Nations (UN) station.

Bus Routes:
Any that passes through Taft Avenue/Mabini/M.H. del Pilar/Luneta

Jeep Routes
Along Taft, ride a jeep to LRT/Taft, and get off at U.N Avenue.

How to get to Manila Ocean Park from LRT-1 U.N. Avenue Station?
1. Cross Taft Avenue, towards Times Plaza.
2. Turn right, and continue walking about 1 block along Taft Avenue (following the LRT1 track) until you get to Teodoro M. Kalaw.
3. Turn left at Kalaw, and continue walking until you get to Parade Avenue/Quirino St. You will pass by the Department of Tourism, the National Library, Old Luneta, Rizal Park, Museo Pambata, and Museo ng Maynila.
4. Turn right after Rizal Park/Museo ng Maynila. You will see Manila Ocean Park on your left behind the Quirino Grandstand.