Starting "Fade to White" is as easy as going to the entrance to zone in through the market wards in Uldah or "the dunes". Select merchant wards and you will be ported into the Waking Sands, which is the headquarters of "The Path of the Twelve". Upon porting in you will see a familiar face and be in a cutscene.
After the cutscene is finished walk ahead straight down the long corridor until you approach a door, go into your menu to open it and it will trigger another cutscene with Minfilia.
After this cutscene speak to her again to trigger another one. At this point you should have another one of those "flashbacks" or "echoes" as they call them. For some reason I caught myself giving her the bitch stare.
Speak with her again and she will ask you whether you agree to be a walker, select agree abd you will trigger another cutscene.
After the cutscene head back down the corridor to the entrance and speak to Tataru the little lalafell near the summoning bell. You are then guided to start the process of chosing a companion.
Tataru will then give you a new NPC linkpearl and tell you to wait for Minfilia's decision about your companion. To trigger the next event simply zone out of the "merchant wards" and run to the Uldah Adventuring Guild. Your linkpearl will then glow and you are told to return to the "Merchant Wards". Zone in and speak to Tataru again and she will make the introductions between you and your companion and you will be promted to select a name for them.
Your companion will then suggest you go meet up at the The Quicksand (Uldah Adventuring Guild). Go there and speak to Momodi to trigger another cutscene.
Enjoy a cutscene with you and your new companion and select the option to begin your next adventure. You and your companion will then part ways and you will be rewarded with 60,000 gil.
Hope this walkthrough was helpful, see you again for the next questline at Rank 26!