we are in drought conditions and my hosta's are turning brown,,,are they dieing or going dormant?

no, they aren't going dormant. They are not getting enough water. If they are then they are getting leaf scorch. Leaf scorch is basically leaves burning up because of you watering when the sun is out in the mid day. Simply water some more but in the evening or early morning. The specific hours are 6-9am in the morning. And 7-8pm in the evening. Hostas go dormant around October-November.

Try to provide as much water as possible, otherwise it will die. Several crops were killed across United States because of severe drought, which is worse than 1988 drought. However, experts say better to follow some ideas to overcome drought. Ideas are mentioned in the following article - http://www.rosebudmag.com/120-hydro-pop/4201-recor...