A pyramid is a three-dimensional solid form made out of triangles, and sometimes a square. There are two common kinds of pyramids: the ones that are made by fitting four triangles together, and the ones that are made by fitting four triangles together on a square base, like the one in the picture here. The pyramids of Egypt are the kind with a square base. You can also have pyramids with hexagonal or octagonal bases, or however many sides you like. If the base is a circle, then the resulting solid shape is a cone.
To calculate the surface area of a pyramid, you need to calculate the area of each of the triangles (or the triangles and the square) involved and then add them together.
To calculate the volume of a pyramid, first calculate the volume of the rectangular solid around the pyramid. That's the area of the base multiplied by the height of the pyramid. Then divide that by three, because the pyramid doesn't fill up the whole volume of the rectangular solid around it.