How to burn hex code program file into AT89S52?
Unless the AT89S52 has a bootloader burned into it (unlikely) you will not be able to program it through the serial port. 

Your board has an ISP header on it which is used to program the MCU. You need an interface cable and application designed to program Atmel MCUs via ISP, eg. Ponyprog. 

If your computer has a parallel printer port then you can use the simple circuit found here:-



If you only have USB then get a USBASP and use AVRdude as described here or ProgISP as described here.