Probably the easiest way to replace the hinges on an existing door is to leave the door hung on the jamb (frame). Start at the top and remove the first hinge on both the door and the door jamb. Install the new door hinge in its place. Do the same on the middle and bottom hinge. If you remove the door and remove all hinges and then replace them while it is not hung, it will be much more difficult to get the job done and harder to get all the hinges to align and work properly.
If you are replacing a house full of hinges to get rid of the old brass or painted over hinges, you'll want to consider using a cordless drill with a screwdriver tip. At 6 screws per hinge on average and 2-3 cabinet hinges per door, your wrist will be tired by the time you are done without the use of a drill. If a screwdriver is all you have on hand, it is still a good way to perform the task. Upgrading your old door hinges can help your door operate smoothly but can also give your home an upgraded look.