OK, well, once you remove the door card, you will see a rubber type cover which is held in by a plastic clip. You will see it on the bottom right corner of the plastic cover shown in the image below.
Make sure you pry it out gently without breaking the clip, but, with enough force to pop it out.
You will then need an allen key, not sure what size, i can't remember off the top of my head to loosen the allen key screw and remove...it's a two stage screw where you can loosen it, pull it out a little, and then you can unscrew it the rest of the way and take it out. Be careful not to drop it in the door otherwise you will be fishing with your fingers trying to get it out.
A picture of the allen key screw and it's location is below...
Next, hold the door open, pull on the door handle, and wiggle out your lock and lock cylinder...your lock cylinder itself is probably fine, but, all the guts holding it together from behind has broken apart.
Once it's out you can take off the plastic cover that is on the lock cylinder...
Now you can put the black cover on your new lock cylinder, and put it all back together.
Any questions, let me know...Cheers and Good Luck