A two speed motor is just that, it has two different speeds. Typically speed configurations are 100% and 66% or 100% and 50%, ex. 1800/1200rpm, 1200/600rpm. They are available in single and two winding configurations.
Not all part-winding motors are rated for continuous operation at different speeds. Most part winding applications are for "reduced voltage" starting at a low speed and full operation at a higher speed.
Depending on the type of 2 speed motor (there are several), you may need to always start in low speed and switch to high speed. You may also be required to have a time delay for going from hiogh speed to low speed so that the motor can slow down to below the low speed before being allowed to reconnect the low speed windings in order to prevent a severe voltage spike. First determine the type of 2 speed application: constant torque or costant HP; it makes a difference.