Today I purchased a new motor and variable speed switch for my old
model 3080 range hood. The speed switch was not the exact replacement;
it had just two wires, and I am guessing that the old switch had many
more contacts than that.

Ok, here it goes. I couldn't figure out how to wire in the part called
the choke coil, which looks like a transformer, so I connected the
switch more or less like this: hot to switch to motor outlet to
neutral. How would include the choke coil in the circuit with its 4
wires, or is it impossible to do this with the new switch I bought?

By the way, the new switch does give variable speed to the motor, but I
hear that the choke coil is necessary to keep the switch from
overheating.