How do you count sigma and pi bonds?

To count sigma and , first you need to know how many single, double and triple bonds are present in the molecule.

A single bond contains one sigma bond (direct head-on overlap of orbitals).

For example, the ##"C-C"## sigma bond in ethane is formed by the head-on overlap of two ##sp^3## orbitals. The C-H sigma bonds are formed by ##s"-"sp^3## overlap.

A double bond contains one sigma bond and one pi bond (side-on overlap of ##p## orbitals).

In ethylene, the ##"C=C"## double bond consists of a sigma bond and a pi bond. The sigma bond is formed by the head-on overlap of two ##sp^2## orbitals. The pi bond is formed by the side-on overlap of two ##2p## orbitals.

A triple bond contains one sigma bond and 2 pi bonds.

In acetylene, the ##"C≡C"## triple bond consists of a sigma bond and two pi bonds. The sigma bond is formed by the head-on overlap of two ##sp## orbitals. The pi bonds are formed by the side-on overlap of ##2p## orbitals.

It's just that simple.

Here's a video on counting sigma and pi bonds.