Count the number of faces on your prism. Since edges are defined as the sides where faces meet, this will help give you an idea of how many edges you will have.
Mark the sides where two faces come together. These are your edges.
Count all of the marks you made and this will be your total number of edges. For some geometric prisms, you can simply count the number of faces and either multiply, add, or subtract a number to find the number of edges. For example, for cubes and rectangular prisms, count the number of faces and multiply by two to get the number of edges. For triangular prisms, count the number of faces and subtract one to get the number of edges.