There are not very many characteristics to a prayer of thanksgiving. The main thing to remember about such a prayer is that it is different than a praise prayer. A praise prayer thanks God for the general state of your life and for his goodness. By contrast, a thanksgiving prayer is about a specific thing. If something good happens to you and you thank God for it, that is a thanksgiving prayer. So the characteristics of a thanksgiving prayer are simply that it is a prayer in which you thank God for specific things that have happened that have made your life better and for which you are thankful.