Check the TX and RX lines on both units. Make sure you connect an input to an output.
On some devices a TX line can be an input on others an output, it depends on how the device is classed.
Start of with TX and RX unconnected. Use a scope or LEDs to see that your TX produces flashing, if not try the RX. On the arduino the RX is an input and TX an output. It might not be the same on your adapter.