How do I attatch a Sony Z1 to BNC cable???

By BNC do you mean SDI? If so you could use a Component to SDI converter using the Z1's HD component out, Blackmagic makes a mini-converter for around $495, or if using firewire Miranda makes a DV to SDI bi-direction bridge for around $1800, you could do a net search for a IEEE1394 to SDI bridge there maybe something cheaper.

If (IF) you are doing a multi-cam array connected to a video switcher set-up, then, yes, simple BNC cables will work (there ARE higher-quality ways to do this, but the BNC cables are a basic method.)

Regardless, the composite video output from the Z1 is a TRRS (Tip, Ring, Ring, Sleeve) 1/8" jack.
(Yellow jack marked "Audio/Video")




So to convert this to a BNC video cable:
You first need an A/V cable designed for the camera (commonly an 1/8" TRRS male on the camera end,
and terminating at the other end in an RCA plug for the composite video (there will also be two RCA audio plugs, as well.)




Add an adapter with an "RCA female to BNC male" (commonly available)

http://www.radioshack.com/product/index.jsp?productId=2104082


Plus (to change the gender to match a BNC cable's plug)
a BNC Female-to-Female "bullet."

http://www.radioshack.com/product/index.jsp?productId=2062625


Then, connect that to the BNC cable.