A LINEAR power supply begins with a power transformer, followed by a rectifier, filter capacitors and some means of voltage and/or current regulation so that the 'load' sees the same voltage regardless of demand.  Below are four versions of regulation all using the same rectifier type: half wave (HW), voltage doubler (VD), Bipolar (BP makes two voltages).

FIGURE-1a: A voltage-doubler derives two voltages from a single transformer winding.  Keep in mind that the transformer's voltage specification is always RMS.  The output of the AC-to-DC conversion - before regulation - will be load dependent, but unloaded could be as high as the AC input (from the secondary) divided by .707 (the square root of 2 = 1.414, which when divided by 2 = .707), quite simply about 70% of the area of the sine wave.  The zener diodes will clamp at a specific voltage, this is also known as a shunt regulator.  Note that the zener diodes are reverse biased (avalanch mode), while the LEDs are forward biased.

Figure-1b: In this regulator, the zener diodes are now used for reference only (by the "pass" transistors) so that load changes do not affect the voltage drop across the resistor.  Because the base-emitter junction loses 0.6 volts, the zener diodes must be 0.6 volts higher than the desired output voltage.

Figure-1c: "Fixed" 78xx and 79xx voltage regulators are substituted for the zener diodes. The TO-220 case style is the more popular packaging.  The "XX" refers to the regulator voltage, the common voltages range from 5 volts to 24 volts.

Figure-1d:  The LM 317 and LM338 are positive and negative adjustable regulators, respectively.