This service kicks in after completing the initial three quests.
In addition to Item Delivery Services, using an East Empire Relic inside of a dungeon will cause the East Empire Company to claim that location in the name of the Outpost for the Hold that dungeon is in. This will begin occurring with the next dungeon the player uses an East Empire Relic in after the quest “East Empire Services” is completed.
Upon exiting the dungeon, a message in the top-left corner will indicate which hold’s Outpost has claimed the location. Banners will be placed on either side of the point the player exited the dungeon as well. If the player returns to the point they exited the dungeon later, after the entryway in the world has fully unloaded, some amount of East Empire Guards will be sandboxing near that entrance. On the inside, they will find East Empire Miners working at any ore nodes within, as well as East Empire Guards patrolling around.
After establishing the third Outpost and speaking to Sha'khar, he'll tell the player that they can begin extracting resources from claimed locations, which will result in bonus resources generated for the player at the associated Outpost.
The resources generated are based on several factors:
Every 3 days in-game, all Outposts will deposit their reward tables to their East Empire Delivery Container.
The EEC Ledger will be updated to reflect the number of claimed locations (divided into Mines and Sites), number of times shipments have been extracted (multiplied by number of sites), and the percentage of those items the player is receiving.
In order for a location to be claimable, it must be flagged as Clearable and have the keyword tag LocTypeDungeon. Most base game dungeons qualify for this by default, but some require a patch to be claimed as they weren't configured properly in the base game.
The Unofficial Skyrim Patch correctly flags most expected locations in a way that makes them claimable. The location must also have a container available for a relic to be used in; some mines in the base game lack any containers - and the East Empire Modified Patch adds a container to those.
For more details, including lists of claimable locations, check out this ongoing forum thread, which we'll keep up to date with known claimable locations.