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!