For a triangular pyramid, aka tetrahedron, you will need the pattern shown in the image. Fold upward along every line shown, and glue each light blue flap onto the adjacent triangle, on the inside of the pyramid. That's all it takes!
You can make an asymmetric tetrahedron as well. Take any triangle, and find the mid points of the sides. In the figure, these are the red dots. Now connect the midpoints to form a smaller triangle. Add flaps, and proceed as in Step 1.
To make a square pyramid, you draw a square base, and attach equilateral triangles to each side. Using the flaps, glue the triangles together so that the the top of the figure is a point where 4 triangles meet.
You can make the pyramid taller by using steeper triangles. Just make sure that the triangles are identical, otherwise they won't meet at the top.