If you notice at the top, there is a handy dandy nut (if you will) that you can unscrew. Take that off, and you're half way to removing it.
After that, you can unscrew the bottom of the p trap from the rest of the pipe.
Next you will need a PVC P trap kit. Make sure you bring your old pipe to the hardware store and check that you get the correct size (Most kitchen sinks are 1 1/2 or 1 1/4 in.)
Figure out the correct orientation of your p trap. The long pipe included should fit inside of the existing metal pipe nicely. If not, shorten it a little bit with a hack saw. Careful though, the pvc is fragile and easy to crack!
You should be able to save the original section of pipe you unscrewed first if you disconnect it from the sink. (See red arrow) The PVC part of the p trap should screw nicely into the green arrow part of the pipe. You may need to use the original nut, but if that doesn't fit, use the pvc one included in the kit. Make sure it's tight!
Have fun!
A suggestion, I don't know if this would work out or not, you'd have to experiment ... Rip the pipe lengthwise with the circular saw first, flip it over and rip it again - now you have your half pipes. Stack those, and cut them with the reciprocating saw or the hand saw. It will be easier to handle.
You'll get a lot more done if you bring something to hold the pipe while you cut it, don't forget about that.
I agree with the suggestion to use a hand saw, but get a BIG one. Even if you're not very fast with it, it will be faster than the power tools once the battery dies.
Best Answer
Inspection cameras often incorporate a transmitter which allows you to pinpoint the camera's position with a separate sensor. The typical use case would be locating a defect under a slab or in the ground so you know where to excavate, but there's nothing to prevent you from running the camera down the waste pipe and locating it in the wall that way.
Of course you can often save the rental cost by measuring from known points, educated guesses based on the structure, or listening for a snake banging around in the pipe.