While many people recommend the hot-pin method for piercing doll ears (heating a safety pin until it's hot, then pushing it through the plastic) I found that it melted the plastic unevenly and left a black soot mark. Drilling them with a miniature hand drill instead leaves a perfect hole with no jagged edges, very clean and uniform. This will work on any type of plastic or vinyl doll - Blythe, Middie Blythe, Pullip, American Girl dolls, etc.
To get started, you'll need a pencil, a miniature hand drill, and a small drill bit. The drill bit should match the size of the hole you want. You can also use a power drill, but it may be harder to hold it steady for such a tiny hole.
For American Girl and Blythe dolls, the posts on their stock earrings are a much larger gauge than people-sized earrings. If you want them to be able to wear stock earrings, you'll need to use a bigger drill bit. I chose this size to fit 22- and 24-gauge ear wires.
Using the pencil, make a dot where you want the piercing to go.
Start drilling, making sure you're holding the drill bit straight and not at an angle. Little twists of plastic will start coming out the sides. Once you've gone all the way through, remove the bits of plastic and you're done! This method leaves a nice round hole with no black soot and no build-up of melted plastic to scrape off.
One of my Pullip dolls, Cornice, came with factory piercings and earrings that go through the ear lobe instead of into the head. You could also make these using the hand drill.
Just add some earrings and you're done!