Barbara, you spackle over nail holes and other "defects" is the smooth wall surface. Most spackles dry pretty quickly and then you sand the area flat, using either a sanding block and sandpaper or one of the new sanding sponges. Those really work great. To apply the spackle, you use a putty knife and, for me, getting a good one pays off. The cheapie plastic ones are OK for other things, but a good one will last forever just doing spackle and this will not be the last time you paint, I'm sure.
The can of primer should have the info on how long to wait before painting. One of the biggest help lines you have is the labels of the products that you are using. Most of them have very complete instructions. People like Zinnser make at least 4 totally different kinds of primer and the instructions will be different for each one. It's a good idea to recheck these occasionally even when you have been painting a long time.