Switch to the 6" taping knife and continue applying joint compound in smooth swaths, working both side to side and lengthwise along the repair lines, until you have a flat, uniform layer that feathers over onto the existing ceiling. Pic 1.

Your layering should completely conceal the mesh tape; pay particular attention to overlapped corners where it is thicker—the idea is to blend the new piece with the existing ceiling so the repair isn't obvious. Pic 2.

Use joint compound to fill the slight depressions over each screw and any blemishes in the surface of the new piece. Pic 3.

Now STOP and allow the joint compound to dry thoroughly before sanding and applying a skim coat, popcorn mixture, ceiling texture, or paint. Allow at least 24 hours to dry thoroughly under most weather conditions.