Follow the story marker to the statue of water bearer by the river. Activate the marker to begin the quest.
Follow the path down and, when prompted, use your Wraith vision to detect and walk through the barrow door.
Here you'll relive one of Cel's memories. Your goal is build your wrath by killing orcs, then kill another ten enemies with your Elven Rage attack.
There's no real trick to the first part- just keep killing, and counter any incoming blows. When you enter Elven Rage, the important thing is select enough targets- wheel around the area and click on anything that's ugly
With your rage sated, the cutscene ends (badly, for Cel), and you return to the cavern, with your earned goodies. If you didn't earn them all, you can immediately retry, either from the menu, or by coming back to this place later and activating the marker.
Note that completing this is one of your first opportunities at grabbing a Gem- a general power-up item that you'll always find useful in your ongoing battle.
Also note that you'll be back here for the Ithildin Door, once you collect all the local sentence fragments. The barrow is also the place where other Shadows of Memory quests in Minas Ithil will appear after you've played them once. You can return here to retry them again and again.