What's the proper procedure of making ghee?
You can start it on high, until it is completely melted, and foaming, to save time.  Then reduce to a slow simmer to evaporate the water.
You want all of the water to be evaporated&mdash;this is critical to the shelf life of your ghee.  

This is indicated by the solids beginning to brown and the cessation of bubbles as you noted; the milk solids cannot brown until all of the water is evaporated.  This is because as long as water is present, it will prevent the temperature from rising to the threshold required to brown the milk solids.  Once the water is evaporated, the temperature in the pot will rise past 212 F / 100 C, and the browning can begin starting around 250 F / 120 C (IIRC).  

Side note: Although I have not seen a traditional recipe recommend it, I imagine it would be very effective to use a candy or deep fry thermometer to monitor when the temperature passes 212 F / 100 C by a reasonable margin.  

You will be leaving the browned milk solids behind, so they will not be in your final ghee.

This typical recipe describes this part of the process as follows:


  Let the butter simmer for up to one hour. Keep an eye on it and keep
  the flame on your stove as low as possible. The ghee is done when you
  see browned butterfat caramelized on the bottom of the pan and the top
  portion of the ghee is clear.


To completely remove the water, you want to continue to heat, until no bubbles remain.  As sarge_smith kindly points out, once the agitation from major boiling completes, and the solids settle, local conditions directly in contact with the bottom of the pan may allow some browning, while a small amount of water remains in the ghee.  
Store your ghee in a sealed container not exposed to oxygen, preferably opaque or in a cabinet to prevent ultraviolet light from reaching it, both of which contribute to rancidity.  Refrigerating smaller quantities doesn't hurt, but when sealed for long term storage, ghee should be shelf stable for at least a year, assuming you evaporated all of the water.  Even if you are worried that some water remains, you should still easily get a month of shelf life, longer in the refrigerator.


See also:
Should ghee be kept out of light?