As others said, it's one piece per week, but all pieces drop out of all 4 raids.

1:1 conversion = 1 Asphodelos ring will get you 1 accessory from the NPC in Radz-At-Han.
2:1 conversion = 2 Asphodelos helms, 2 Asphodelos gloves, or 2 Asphodelos boots will get you the 1 respective piece (helm, gloves, boots)
4:1 conversion = 4 Asphodelos body pieces or 4 Asphodelos pants will get you 1 body or 1 leg piece.

If you want to get hands and feet the first week you run it, roll for those pieces specifically, tell the group you're running with what you're after to see if people are just rolling on whatever or are wanting something specific, and hope you get the drop. You can run each raid, 1-4, until you actually get a drop into your inventory.

Also, every time you finish floor 4 for the week, you will get a Blade of Asphodelos as an extra drop. In 7 weeks, you will be able to get the tomes to turn in to get a weapon from the tome vendors. After the restriction is lifted at a later time (usually next major patch, so 6.1 or thereabouts; sometimes the Blade drop restriction will be lifted later) you can get all pieces as many times as you want, and every time you clear floor 4 after you'll get the Blade drop. Patch notes will always tell you what is coming off of a restriction, so look ahead once they're out. The 24-man raids will have similar restrictions on the loot, and will also drop something to augment the current tome gear once a week as well.