This is much the same as the fruit of the spirit, as shown in Galations 6
When we realize what the spirit is, as shown on this page: The Spirit, determining the evidence of the Holy Spirit in the life of a believer becomes simple. It is basically seeing a person who is living an honorable, noble, loving, compassionate, truthful life. (more later)
One the strongest evidences sthat we can see is a person living a righteous (right acting) and godly (living in harmony with god and man) in the midst of intense trials and adversity. Anyone can act good for a while when everything seems to be going our way. The true test of what living by the spirit is how one thinks and acts when everything seems to be going against him. Will he hold the course (of doing what is right) no matter what happens?