Yes wire it straight in and either enable the internal pull up resistors or add an external one of your own. Don't forget to also connect the grounds of the two systems together.
My exprience is that some PIRs will not work reliably with just the internal pullup of the input pin. Be prepared to add an additional 10K pullup as well.
The receiver requires a 12v supply. I was going to use same supply which supplies the arduino. I have a 12v 2a power supply. This would mean ground is common.
So the open collector from the receiver on the diagram would connect direct to the input pin on the arduino ? (within internal pull up resistor on)
"So the open collector from the receiver on the diagram would connect direct to the input pin on the arduino ? (within internal pull up resistor on) "
Yes. Additional pullup to +5V may be needed also, try it & see how it works without it.
I'd double check it doesn't have a 12V pullup already - the output voltage on the open collector output shouldn't be reading more than 5V in either state when unconnected - Arduino pins don't like being pulled outside its 5V supply range.