As with regular tattoos, your skin will be punctured over and again with a needle. The side effects will also be similar to those from a regular tattoo, but there will be additional ones, too.
The area tattooed (or 'made up') will experience some swelling for a few days. You can use cold compresses to bring down the swelling, and you will also want to use antibiotic ointment to combat any risk of infection in the area. If you've had something done to the eye area, you won't be able to wear contacts for several days because of bruising and swelling.
Something extra to be aware of is that the results of permanent makeup will not at first appear the way you want them to. The color will be darker for an average of a week to ten days, but it will fade a bit during that time and the shade will gradually become the one you chose. If you're displeased with the results during that time, just wait a bit to see how it looks after ten days or so before you panic. Sometimes your permanent makeup can take up to three weeks to fade to its final shade.