In Deep Slumber

Hint: you have to use [spell=88423] in order to clear the first room.

This quest isn't really that obvious about what to do right away.
If you have problems this is a short how to:

1. Run up and dispel his root with [spell=88423] (yes you have to be in Resto spec).

2. Stealth past the mobs and wait over at the ramp next to the roots. Don't swim in the water or touch the red stuff what so ever (it bumps the bar up quite a bit).

3. As soon as the roots are removed use Dash and sprint all the way up. Avoid all the red stuff on the ground and the mobs.

4. When you get all the way up and see mobs outside, stealth and go to the objective. Those trees roots you constantly. I still made it by shape shifting myself all the way over there though so you're not doomed if you mess that up.

Tip: You'll most likely fail a couple of times. Sometimes when you get out of the dream your HP is dropping rapidly. Be ready to heal!

Preparation:

1. 
   
2. Go into Resto Spec (sounds obvious, but it may be you are doing as your off spec like me!) and set it up if you haven't already done so
3. 
   
4. Set up your kitty form so you can easily dash/stealth
5. 
   

The entrance to the quest is through Tel'Andu Barrow Den, in the north of the Dreamgrove. Naralex is at the bottom (if you remember the moving Staghelm quest from cata, the same sort of barrow location, but go in and turn left).

The route up needs to dispel roots on the druid, using stealth to get past the mobs and healing yourself to get out.

1. 
   
2. Go into kitty form when taking the quest and then stealth past the first mob.
3. 
   
4. Next to the first mob, turn right and use Nature's Cure to free the druid from the roots.
5. 
   
6. Heal yourself to reset the bar (if needed) and put some HoTs on to keep it low over the next bit
7. 
   
8. Go back into stealth and go to the route up out of the den
9. 
   
10. Don't wait for her to come and dispel the roots barrier, just jump over the rocks next to it
11. 
    
12. Heal yourself if needed to reset the bar again and HoT up
13. 
    
14. Back into stealth and dash past the mobs, avoiding their trails which will damage you
15. 
    
16. When your reach the exit, open your map to check where the item is (in the circle in front)
17. 
    
18. Heal/HoT and back into stealth
19. 
    
20. Keep to the left to avoid the corrupted treants
21. 
    
22. Click on the staff in the centre - it should be sparkling slightly
23. 
    
24. Click on Lyessa next to it and she will return you after a bit of a speech
25. 
    

(Many thanks to the other posters for all the hints especially: karlthepagan - Dispel; ehrw stealth and dash; n0one for jumping over the rocks; and takstol about healing ... which should have been one of the most obvious things about this quest for us off-specers!)