How to place figures side by side in latex and their captions as a and b, with another common caption as figure 1...?

As suggested in the comments, just use a tabular with the numbering manually inserted; this is a fairly good solution as there's no mention of the subfigure numbering to have the main figure number included.

The example below was taken from the ws-ijcm class source:

begin{figure}[th]
  centering
  begin{tabular}{ c @{quad} c }
    includegraphics[width=10em]{example-image-a} &
      includegraphics[width=10em]{example-image-b} 
    small (a) &
      small (b)
  end{tabular}
  vspace*{8pt}
  caption{A schematic illustration of dissociative recombination. The
  direct mechanism, 4m$^2_pi$ is initiated when the molecular ion
  S$_{mathrm{L}}$ captures an electron with kinetic energy.label{one}}
end{figure}

Referencing the main figure would use the regular Fig.~ref{one} approach, while subfigures can be referenced in a similar way: Fig.~ref{one}(a) (for example).