You can check whether the serial port connections are working correctly using a serial loopback.
A simple loopback consists of connecting RXD and TXD together. These are pins 8 and 10 on the Raspberry Pi GPIO header, or pins 2 and 3 on the standard RS232 D9 connector on the USB-RS232 adapter:
Serial loopback connections to test the Raspberry Pi GPIO (left) and RS232 9-Way D connector (right)
An RS232 full loopback cable also connects pin 4 (DTR) and pin 6 (DSR) as well as pin 7 (RTS) and pin 8 (CTS) on the RS232 adapter. However, this is not required for most situations, unless these signals are used. By default, no pins ...
