Hi,
BNC is simply a physical connector. The antenna needs to connect to a 434 Mhz receiver of some type. You may need to adapt the BNC to whatever input connector the receiver has, but that has nothing to do with Arduino.
Once the receiver (and I assume it's RTTY demodulator) is putting out data, THEN you will need to connect that to Arduino or a PC..
Read up on RTTY (Radio Teletype). You need to know stuff like how many data bits per character etc...
There's details to this!!