That is a relatively modern ATCO, nothing like the one I was guessing you had. There appears to be a spring-loaded button on top of the float bowl for flooding it, which would be the way you get cold-start enrichment. I suggest you trace the Bowden cables from the two clutch-type controls to see where they connect - most likely one will be an engine clutch (drives everything) and the other a rear roller (drum) clutch. The engine clutch would be under the tin cover over the engine output shaft. A drum clutch (if that is what the other control does) would be inside the left-side chain case, but the cable would probably go into the case from the right side of the mower's side-plate.
If you find out which handle does what, you will know how to disengage the clutch(es). With them disengaged, you start the engine by setting the throttle about mid-way, flooding the float bowl, winding the starting rope around the pulley on the right side of the engine, and pulling. If all is well it should start immediately.
The mower badly needs cleaning. If you do that you will find out more about what goes where and what it does.
