OK, U R right on the money with your connections; TX goes to TTL in & RX to TTL out.
The corresponding RS232 output goes to pin 2 on the DB9 connecting to the PC & RS232 Input to pin3.
You also have to connect the signal GND wire (pin5) on the DB9 to GND pin on the HIN232CP (pin 15). Don't worry about the handshaking lines. As long as you don't send large amounts of data at high baud rates you should be OK.
Also try to select a baud rate that yield the lowest error preferably less than 1%. Some peripherals and computer ports are a bit sensitve. Consult your data sheets; there should be baud rate tables for different OSC frequencies under "USART" section.
If you sometimes get jibberish or part of your string are missing on HT, use a 4ms time delay like for an LCD.
To test with Hyper Terminal, just create a new session. In properties under the "Phone number" tab select the com port you want to use. Click "configure" & choose the same baud rate you selected for the PIC. Data bits = 8 Stop bit = 1 no parity no flow control. Under the settings tab select "Ansi" emulation. Make sure under "ASCII setup" that "force incoming data to 7 bit ASCII" is unchecked.
Click "OK" everywhere you need to, to get back to the terminal window.
Any incoming data from your PIC will now be displayed as it is sent. Anything you type will be sent to the PIC.
If you are using assembler, I can help you with your code; haven't tried C yet
Hope it helps