To learn how to apply the Marching Cubes algorithm in 3d here. Or if you want to jump ahead to an improved technique checkout Dual Contouring.

to know which the edges are that we have intersections with so that we can start adding triangles.

The algorithm begins by determining the configuration of the cube, by comparing the value of our cube at every corner vertex with the isosurface level. 1 2 3 4 5 6 7 8 9 int cubeIndex = 0; if (cubeValues[0] < isolevel) cubeIndex |= 1; if (cubeValues[1] < isolevel) cubeIndex |= 2; if (cubeValues[2] < isolevel) cubeIndex |= 4; if (cubeValues[3] < isolevel) cubeIndex |= 8; if (cubeValues[4] < isolevel) cubeIndex |= 16; if (cubeValues[5] < isolevel) cubeIndex |= 32; if (cubeValues[6] < isolevel) cubeIndex |= 64; if (cubeValues[7] < isolevel) cubeIndex |= 128;