My husband took care of this by spackling the drywall. He filled the gaps and spread the spackle out beyond the holes. He held the putty knife at an angle and faded the edges of the spackle out along the wall to make everything nice and smooth.
Then, he put a latex primer on top of the spackle. We let that dry overnight before painting the walls. I was very happy with how smooth they looked after being spackled and painted.