The Mage job change takes place in Geffen, inside the Mage Guild building. First you must be a Novice with Job level 10 and all Basic Skills learned. The Guildsman gives you a random assignment: brew one of four Mixed Solutions on a special machine following an exact recipe. Once you gather the ingredients and mix the correct solution, you bring it back to the NPC and instantly become a Mage.
Mage Guildsman NPC (164,124). Pick "I want to be a Mage" and sign the application — he gives you one 
Empty Test Tube and a random task: brew Mixed Solution No. 1–4.
Jellopy, 
Fluff and 
Milk, which solvent (Payon or 
Morocc Solution), the Magic Powder serial code and the catalyst gemstone.
Payon Solution from 
Dollshoi (pay_arche 122,100) or Morocc Solution from 
Ponka-Hontas (moc_ruins 91,150) — each costs 50 Zeny and one Empty Test Tube.Jellopy and Fluff drop from low-level monsters, Milk is sold by NPC shops.Jellopy/Fluff/Milk, enter the Magic Powder serial code and pick the catalyst gemstone as the recipe specifies. The machine produces the finished Mixed Solution (a wrong recipe yields a faulty one and you must redo it).Mage Guildsman with the correct solution. He checks it, takes it, and instantly changes your job to Mage, plus 50 Zeny.