Count all single bonds as sigma bonds
Count each double bond as 1 sigma bond and 1 pi bond
Count each triple bond as 1 sigma bond and 2 pi bonds
Add all sigma bonds from every bond in the structure
Add all pi bonds from every double and triple bond in the structure
For rings, count the bonds the same way as open-chain structures
For resonance structures, count sigma and pi bonds in one valid Lewis structure
For aromatic systems, count sigma bonds along the ring framework and pi bonds from the conjugated double bonds or delocalized electrons
For coordinate covalent bonds, count them as sigma bonds
For bonds to hydrogen, count each as one sigma bond
For lone pairs, do not count them as sigma or pi bonds