You connect GND and GND together, Tx to Rx, and Rx to Tx.
I don't know how much power the Propellor board takes, but if it's 3.3V at no more than 50mA then you can connect 3.3V from the Pi to the 3.3V line on the Propellor.
For low-level "send a byte" stuff, you don't need any special library. In 'C' you use standard system I/O calls. For Python you can use pySerial (I just googled that - I've not used it). You will also need to set the baud rate/data bits/partity/stop bits on each device to match.
Nobody can advise about higher level libraries without knowing how you want to use the serial link.