Having a personal relationship with someone in need of therapy can be quite difficult.  The constant worry, the unpredictability of their behavior, their destructiveness (for some), and a lack of knowing how to help, can cause great distress and a desire to just run away.  Here are some suggestions to help you cope and remain supportive.
A. Knowledge is Power!
Learning more about your friends condition/mental state can be very helpful in terms of being able to predict their behavior and mental state.  Predictability will reduce your own stress.  There are many websites that explain the mental and behavioral patterns exhibited by people with certain conditions.  For a more in depth understanding, there are many popular books published every year about people with certain conditions.  
B. Be a good friend…but not a therapist!
The best thing (although not an easy thing) is to be supportive of your friend.  A supportive friend is there to help in many different ways:
​1. Letting them know that you care about them
2. Being there to listen.  
This means to be open when your friend brings up the topic of their mental state.
This means resisting when you feel like you can simply solve their problem with a single suggestion
C. Find your own support
Support groups can be helpful for both the individual seeking treatment, and you, as their friend or relative. They can represent both sides of the matter and provide an outlet for expression, as well as information regarding the particular issue. They are not limited to mental health, and are available in a variety of formats (church groups, clubs, non-profit organizations, or family members of individuals with illnesses).

D. Find your own therapist
In some cases, the constant stress of being supportive of your friend can become overwhelming.  Seeing a therapist, yourself, could be very helpful in this circumstance.