1) Do World Quests in Val'sharah. Most World Quests in this zone awards reputation with The Dreamweavers, but if you are unsure, just use your mouse to hover over the quest and check which factions it awards reputation with. Also note that The Wardens World Quests in Val'sharah gives rep with both the Wardens and the Dreamweavers, so do all of them as well. The same goes for Kirin Tor World Quests in Val'sharah.
2) Complete the dungeons Black Rook Hold and Darkheart Thicket. The endbosses of these two dungeons gives you +250 reputation with the Dreamweavers per kill, so farming these two dungeons can be a nice way to increase your reputation. It's not very efficient, but at least it is predictable.
3) Do Kirin Tor Emissary Quests. Upon doing four of these, you get to pick a faction to increase your reputation with, by + 1 500 rep! So do four of these and pick the Dreamweavers to get a nice reputation bonus.
The Dreamweavers reputation rewardsUpon hitting new reputation levels, more items become available for sale from Sylvia Hartshorn in Lorlathil in Val'sharah. Below are all the reputation items:
Path of Elothir
Leaves fluttering leaves in your wake for 5 min (10 min cooldown).
Tear of the Green Aspect
Summon a vision of the green aspect Ysera (20 min cooldown)
Boon of the Harvester
Permanently enchants shoulders with Harvester enchantment, allowing the wearer to obtain Harvested Goods from the corpses of their enemies.
Treasure Map: Val´sharah
Reveals treasures on the minimap of Val´sharah for 1 hour.
Rank 3 Recipe: Warhide Jerkin (Leatherworking)
Rank 3 Formula: Enchant Ring - Word of Versatility (Enchanting)
Place a Moonfeather Stature on the ground. What´s the worst that could happen (1 Day cooldown).
Pendant or the Moon Temple
Teaches you how to summon this companion.
Seed of Solar Fire
Item needed for the hidden Artifact Weapon Appearance for druids.
Pauldrons of Entwined Roots
Dreamweaver Initiate´s Tabard
Tabard of the Dreamweaver
Rank 3 Recipe: Dreadleather Pants (Leatherworking)
Rank 3 Recipe: Dreadleather Mask (Leatherworking)
Rank 3 Recipe: Dreadleather Footpads (Leatherworking)
Rank 3 Formula: Enchant Ring - Binding of Haste (Enchanting)
Rank 3 Formula: Enchant Neck- Mark of the Loyal Druid (Enchanting)
Rank 3 Formula: Enchant Cloak - Binding of Agility (Enchanting)
Rank 2 Formula: Enchant Neck - Mark of the Heavy Hide (Enchating)