Set Affixes are the Green Affixes. Amethyst Crystal can be used to put Set Affixes on Items. some Sets are Class Specific, so you can only put them on Items of a certain Class (you can then use Jasper Crystal to change the Class to the Class you want). then there are the Sets that can only be found on Items as Loot.
Examples:
Ascendant Set can be placed on Items of any Class.
Pathfinder Set can only be placed on Rogue Items.
Defiant Set can only be found on Items as Loot.
here is a Post that shows most of the Restrictions using Crystals.
if you have more than one Item with the same Set Affix, they add up, like Defiant (2) if you have 2 Defiant items. this is important, as some Set Bonus Affixes require more than one Item with a certain Set Affix to be activated. using Myth Stones or Items with Legend +2 All Sets (+4 total) you can get up to Set Affix (8) with +4 All Sets and 4 Items with the same Set. most players just go with Set Affix (5). this way, you can have seven different Set Affixes (5).
welcome to DQ Forums @Komochi !