1. Find the child and tell him/her that you love and want them to be safe. Offer to drive them to a shelter or connect them with a community resource. Recognize that if the child was upset enough to run away, there must be something seriously wrong. As the parent, you might not be able to find out or deal with the problem on your own. In fact, in the mind of the teen, you might be the problem or reason why the child left in the first place. They therefore probably need someone other than you to help them get back on track.
2. Get professional help. It is easy to blame the child or think that everything will be better if they just come home and you can carry on. It is very important, however, that you have support and the perspectives of someone who can help you get through this in the best way possible. If you are losing sleep and feeling a great deal of upset, you might not be making the best choices or think through things in a logical way.
3. Do not bring the child hone without clear conditions. Pretending won't make it better and going back to the way that things were will likely not repair the situation. In fact, it might lead to repeated incidents of running away or even conflict. This is your house, and you have the right to be respected. Loving does not mean that you should allow the teen to run the show or threaten you or break basic house rules.
A couple of years ago my older son, daughter and I visited Alcatraz Prison which is off the coast of San Francisco. My son purchased a sign for his house which reads "You are entitled to food, clothing, shelter and medical attention. Anything else that you get is a privilege."
Now this may seem harsh, but I know of many parents who work hard and pay all the bills while their teens take advantage of them. They lie around waiting to be served.
It is okay for you to tell your child that if they are going to live with you, they must either go to school or to work. They need to understand that they have responsibilities too and must contribute to the family rather than just take what they without investment.
Yes, if your teen leaves home unexpectedly it might feel horrible at the time. But, on the other hand, it might be the beginning of improve relationships and an embrace of maturity that your teen might not otherwise have known.