I can confirm that this works in PrC 3.3h RC2. As xwarran says, you can write magic using the icon in the Archivist radial menu.
All spells that are Cleric, Druid, Ranger, Paladin, or ANY cleric domain spell can be learned by the Archivist. Only spells from the Cleric domain proper can be learned by level-up, though.
In terms of what level the Archivist gets spells at, it seems to go in that order: Cleric, Druid, Ranger, Paladin, Domain. So if you want to cast Snare (level 2 ranger spell, level 3 druid spell) it becomes a level 3 Archivist spell. Magic missle (force level 2) is a level 2 spell, not a level 1 spell since it is taken from the force domain list as a level 2 spell.
Btw, in case I forgot to mention - Archivist is frekin awesome!!! I'm very excited for the next release so I can play one on the PW I play =).