The circuit you have been looking at doesn't look like it would work anyway - the LDR and variable resistor are the wrong way round!.
If you don't need the COB then you don't need the amplifier either, simply use an opamp as a comparator (a 741 would be fine) and use the output of that to switch a transistor feeding power to your siren.
Figure 12 here does pretty well what you are wanting.
Relays are very simple devices, electro/mechanical rather than electronic, it's just an electro-magnet (the coil) which activates a switch (the contacts), the connection details should be stamped on the relay, or provided with it. They are also very easy to locate using a meter on the ohms range.
For your application, you could replace the relay directly with the piezo alarm you have.
Hello as you can see im very new to electronics (ive had to learn most of it myself )
Now where wud i "Plug In" My Piezo Alarm its go the postivie and negative wires , put i dont see where i plug it in on my board , ive put in the chip and the transistor and what not and that looks ok
Im really stuck on where it has to go
and i also want to fit a switch (which i have) to it , where wud i put that