I have always done it at around 4 months old. They don't even remember it! I had mine done when I was 5 years old, and it was very scary and upsetting, and I remember the pain it caused. My girls don't remember it at all. Because the earrings were there as long as they could remember, they never tried to pull them out or tug on them. I plan to do the same thing with my next girl, due this summer.
My daughter chose to have a second piercing at 6 years old, but that was easy because it was her choice, and she already had the first set from when she was a baby. We made a big deal of the second pair because it was her "big girl" choice, and th first pair was fun because she was always able to accessorize and pick a pair to match her outfits every day, even she she was a toddler. It helped us teach her color matching, too.
To help with the process, I gave them some baby ibuprofin before we went so it would be in their system when they were pierced, and then I made sure to have a bottle ready or be ready to immediately nurse them as soon as it was over. They cried for about three seconds, which was the time it took to get something in their mouths after they were pierced, and that was the end of it. It was an easy experience for us, and I would suggest doing it early to avoid the emotional trauma it can cause for an older child.
I hope that helps. I wish you the best! :)