Finish installing new drywall next to the area where the existing drywall is in place. Tape the seams between the sheets of drywall, and apply a layer of drywall mud over the tape with one of your drywall trowels. Let the initial coat of mud dry.
Set a scrap piece of drywall in your installation area. The scrap drywall will be a test, or practice, sheet.
Determine the type of drywall finish pattern that needs to be matched. Experiment on on only the scrap piece of drywall to achieve that finish pattern. Work the drywall mud across the scrap piece's surface, applying it with a paint roller or trowel. If the old drywall finish is a brush pattern, experiment with drywall brushes on the mud until you achieve the correct pattern. If the old pattern is a random mud pattern, simply trowel the mud on the scrap drywall with various trowels and thicknesses to achieve the random appearance.
Do not attempt to apply actual finish on the new drywall section until you experimented and achieved the desired finish on the scrap drywall. Otherwise, you could be left with a new area that looks completely different from the old area.
Apply drywall mud to the new drywall area once you are satisfied with the finish pattern you created on your test piece. Take your time and work slowly, always putting more mud on the wall than you think you need. You can always remove excess mud with a trowel, but trying to achieve the correct finish pattern with insufficient mud will make your job harder. When the project is a wall, work your way from the bottom up and alongside the old area. If the project is a ceiling, simply start next to the old pattern and work your way outward.