To fill the quiver, hold it in your hand and right-click. This will allow you to place arrows and javelins into the quiver, thereby making room in your inventory. To equip it, place the quiver in an invisible slot next to the chest-armour slot. If you can't find it, shift-click the quiver and it will move to the appropriate slot.
Once equipped, the game displays your current amount of ammunition in the bottom left corner. If you pick up any ammunition on the ground, it will automatically be inserted into the quiver. Javelins in the hotbar will be replaced with javelins from the quiver when thrown, thus making javelins easier to handle.