This is done by flow control as it is called in hyperterminal. It can be implemented as hardware flow control using the control signals of the RS232 port DTR, CTS, RTS,... In this case the uC will wait for the PC to assert the appropriate flow control signal to send data.
Another way is to use a software flow control like the xon/xoff. In this case the uC waits for a byte (xon) to send data and stops sending if it receives a xoff.
Both are standard protocols and you can search the web for detailed info.