A picture would help, can't identify it without seeing it. If it's a black Singer, the usual spot for the serial # is on the bed right in front of the pillar and many have the model on a little plate right below the Singer emblem. Most models of black Singers can be identified this way. If it's a colored machine the model should be somewhere on the front of the pillar.
The controller is probably up under the cabinet in a bracket with a knee lever.
Cari