Here's how we get that:
1. Move the first consonant (or consonant cluster) to the end of the word. "Add" moves to the end of "ison" making "isonAdd".
2. Add "ay" to the end. So we have "isonAdday".
3. The silent "e" at the end of "ison" is removed. Giving us "isonAdday" becoming "isonAdday".
Therefore, Addison in Pig Latin is Addisontonway.