Take that Unidentified Weapon to Dithalion in Rivendell or Wafi in Thorin’s Hall. They will tell you to get it identified by the adjacent Forge Master. You will be seeing a lot of these NPCs for the rest of your time in Middle Earth. Identifying your weapon does two things: You will be able to equip it and its Legacies will be revealed. Legacies are the buffs you can spend points on to increase their Rank as your item levels up.
Equip the Weapon and talk to Dithalion or Wafi again. Now they want you to slot a Relic in your weapon. You have already picked some of these up as quest rewards, but they aren’t kept in your inventory, thank Ea, so you may not have noticed. Click the little sword button (just to the left of the big sword button for auto attack) or press Shift + I.

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This will bring up the Legendary Items window, pictured at right. The tabs along the top (in the yellow rectangle) take you to the different Legendary Items you have slotted. The left pane (in red) lists the Legacies. You can rank them up by clicking one to highlight it than clicking the Rank Up button below.
The right pane (blue) shows your available Relics, divided between the Settings, Gems, and Runes tabs. You can have one of each slotted on each item, and the ones that are slotted in the item you are looking at appear above the pane (orange). Choose one and hit the Slot Relic button below the pane. Do this for each of the three Relics tabs, or as many as you have appropriate Relics for.
Now you can talk to Dithalion/Wafi again, and he will explain that you need to level the weapon up.