Find the surface area of each face then add them together to give the total surface area.
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Face
cross section
There is no standard formula since a polyhedron can have a number of different shapes. A hexahendron, for example, can be a cuboid (6 rectangular faces) or a triangular dipyramid (6 triangular faces) or others. The number of different shapes increases rapidly as the number of sides (which determines the name) increases. The only solution is to calculate the area of each face and add them together.
A net is an arrangement of polygons, joined edge-to-edge, that when folded up, form the surface of a polyhedron.