Most doors have standardized doorknobs, and almost all of them have two large screws that are long enough to reach through/get across(?) the other side of the door. Just loosen them with a screwdriver and take them out. After that, you can take out the doorknob itself. To take out the latch bolt, you have to remove a few additional screws. After that, you can pull it out, and then you'll have an empty hole in your door and you're ready to install the new doorknob. Put the new bolt in, but be careful how you put it in because you don't want to put the latch in backward.

Make sure that it's facing the correct way. Put the latch bolt in and put the screws in. Put the doorknob in. There are long things in the doorknob. That's where the screws are going to go across on the other side. Put it back in. You have to match the holes of the knob of the screws so you can screw them in. Set in the screws, don't tighten them yet, just set them in, because you want to make sure everything is seated properly, and only tighten them when both are set.