How can I obtain 12 V DC, 3.3 V DC and 5 V DC from a single Li-ion cell?
For 3.3 volts a standard linear or buck regulator is the simplest approach. For 12 volts use a boost regulator and for 5 volts tee-off a linear or buck regulator from the 12 volt output. Depending on current taken on each power rail this may change.