You can connect Rx to Tx, Tx to Rx (and Gnd to Gnd if needed) and monitor what each one is outputting via the Serial monitor connected via the USB port.
You shouldn't enter anything from the Serial monitor as that will interfere with the Tx lines, but you can certainly monitor what is happening on the Rx.
I was doing this over the weekend, two instances of the IDE on one computer, each with an Uno.
Used Serial.write commands to send simple messages back & forth. Data from 0x48 up to 0x126 showed up on the moniters as regular characters 0-9, A-Z, a-z, plus some of the punctuation characters. The complete list can be seen as www.asciitable.com