Open the tomb of the king under the mountain.
After Getting inside Erebor do the following.
do n,ne,nw,2n,n,w,2d,2e,se,2d,nw,e,s,2d,se,s,se,2d,nw,e,n,nw,2d,ne,n,w,sw,s,sw,w,scramble over boulder,2n
There are various different senses you can use to examine the gate, try them all. Then use the method you are given to open the gate.
You will need to get inside Erebor somehow by obtaining a key or picking the lock
Once inside this quest there are quite a few freebie items you can collect, because of this most of the time this quest will not need to be completed in order to progress to the other Thrain's Tomb quests as the area will already be open
do feel gate,touch gate,smell gate
These commands (or one of them) will give you a voice inside your head which will tell you the exact command to open the gate, it changes every reset and will look something like:
It keeps repeating the same words, over and over again... Through a decree the locked gate will open.
The relevant part of this is at the end i of the sentence, though you have to transform it slightly, in this case it would become.
decree the locked gate to open
If any of the information here is missing, or wrong, please let us know.