A simple AC powered linear power supply usually uses a transformer to convert the voltage from the wall outlet (mains) to a different, usually a lower voltage. If it is used to produce DC a rectifier circuit is employed either as a single chip, an array of diodes sometimes called a diode bridge or Bridge Rectifier, both for fullwave rectification or a single diode yielding a half wave (pulsating) output. More elaborate configurations rectify the AC voltage at first to pulsating DC. Then a capacitor smooths out part of the pulses giving a type of DC voltage. The smaller pulses remaining are known as ripple. Because of a fullwave rectification they occur at twice the mains frequency (in USA it's 60 Hz doubled to 120 Hz). Finally, depending on the requirements of the load, a linear regulator may be used to reduce the ripple sometimes also allowing for adjustment of the output to the desired but a lower voltage.
More elaborate versions used by circuit designers are adjustable up to 30 volts and up to 5 amperes output. These often employ current limiting. Some can be driven by an external signal, for example, for applications requiring a pulsed output.
In the simplest case a single diode is connected directly to the mains and uses a resistor in series with a more or less fixed load to recharge a battery. This circuit is common in rechargeable flashlights.