A requisition quest is obtained by speaking to a requisition officer in any Inquisition camp and choosing the "Report" dialogue option. To refuse the quest, walk away or choose "Not right now"; there is no penalty in doing this. Details on the requisition will be listed in the quest log. It is possible to have an active requisition for each area that contains at least one Inquisition camp, but only one requisition may be active at any given time for a particular area. Requisitions are assigned randomly, and repeat indefinitely.
The quest can be completed at any requisition table at Inquisition camps, near the quartermaster in Haven or Skyhold. To complete a requisition, click on the table, which will show a list of all active requisitions, then click "craft" to complete it (relevant components will be consumed). Requisitions for which all the necessary supplies are listed will be displayed with white text; those which cannot be completed are displayed red.
Each requisition, with the exception of Skyhold upgrades and Haven requisitions (see below), grants +1 Power and a varied amount of Influence (either 100, 200 or 300, based on the level of the area where the quest is obtained).
(All Platforms) Due to a bug Lore Requisition on the Plains cannot be completed. The items are consumed and the quest restarts automatically, preventing them from obtaining other requisition quests in that area. For pcusers there is an unofficial mod which fixes the issue here.