How is hybridisation of a carbon atom determined by looking at the molecule's structure and observing the lone pair and/or sigma bond present?
The answer you are looking for is probably this:

Count the number of $\sigma$ bonds made by that atom, and add to that the number of lone pairs present on that atom. This number is called the steric number. 

If the steric number is $2$, hybridisation is $sp$.
Similarly, $3 \Rightarrow sp^{2}$, and $4 \Rightarrow sp^{3}$ hybridization.