Vocations are small breaks between Rites where you can do three different tasks:
1) You can forage for items in or around your blackwagon. This could range from sellable goods to perhaps even Talismans.
2) You can study the Book of Rites to give a permanent boost to your party members.
3) You can train an Exile to give them a better understanding of the Rites.
For this, you simply have to do any of these ten times. However, what I would suggest, for another trophy, is to study the Book of Rites. There are 8 upgrades you can get from doing this, meaning after that, you'd just need to do two more to get this trophy. The 7th and 8th upgrades increase your dousing stat, meaning you'll do slightly more damage to any Pyre when you plunge into it (maximum of +2).