Hi

Connecting PC with 8051/52 is simple. IF you have written the code successfully, then you just need to translates the signals to RS232 level on TXd of 8052 and from RS232 to TTL level at RXd. It can be done by several means, but most popular (and easy too) is to use specific driver Integrated circuit. Earlier it use to be 75188 and 75189 for TXd and RXd seperately, but now both are available in one package called MAX232 and many derivatives you will find at your electronic store.
This is necessary because PC's RS232 signal usually swings between +12volts and -12Volts, they are not TTL level. Thats the reason you would require the level-translators.

Rauf